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プレプリどんどん: math.NT

A Mathematics and Science podcast

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arXivのmath.NT (数論) の新着論文の概要をAIで日本語でお届けするポッドキャストです。 情報収集にお役立てください。 (AIで生成していますので必ずしも正しいとは限りません)

Newest episodes

零点とコードと曲面 - 2026/11/11の論文34本

1 hr 4 min

arXiv math.NTの新着論文34本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-11/ The uncertainty operator, the Weil ground state and the zeros of zeta: a numerical study and conditional positivity of the Weil quadratic formThe $\mathbb Q$-gonality of $X_1(42)$ is $12$Bounding the security of the Bromberg-Shpilrain-Vdovina hash functionA counterexample to the Erd\H{o}s--Mahler conjectureA Threshold-Crossing Condition for the Least Colossally Abundant Counterexample to Robin's InequalityOn the equidistribution of eigenfunctions of higher dimensional cat maps modulo prime powersPeriods and CM motives of abelian typeDiophantine approximation with prime denominators in short intervalsA Moment Proof of the Hollman-Xiang Conjectures on Kloosterman PolynomialsWhen do all iterates of $x^2 + a$ have maximal Galois group?Explicit plane models for all Galois quotients of the Hermitian curveA generalized Vojta-R\'emond inequality over adelic curvesAsymptotically good codes from Siegel modular varietiesSun's conjecture on a certain ternary quadratic formA complete classification of permutation binomials of the form $X^r(X^{2(q-1)}+a)$ over finite fieldsThe exponent $3/4$ for the exceptional sets of the equations $K/n=1/x+1/y+1/z$A Complete Classification of Maximal Hyperelliptic Curves Related to Chebyshev PolynomialsCounting Rational Points on Cayley's Cubic SurfaceDivisor Folding and Finite-Group Trace ObstructionsThe distribution of small gaps between zeros of the Riemann zeta functionZeros of Katz's p-adic Eisenstein series E2Cyclically covering subspaces and additive perfect codesA cyclotomic Artin-Tate formula and sphere packing for K3 surfacesNonnegative weak tilings and the Coven-Meyerowitz condition (T2)Non-abelian $p$-adic Hodge theory and stacksDavenport Constants of High-Dimensional Integer SetsParabolic induction and pullback of perverse sheaves on Vogan varietiesThe zero-sum constant $\mathsf{s}_p^*$ and inverse problemInte...

L値とモジュラー形式とランダム代数 - 2026/11/10の論文56本

1 hr 39 min

arXiv math.NTの新着論文56本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-10/ A recursion relation for the coefficients of Swinnerton-Dyer type polynomialsA singular homeomorphism between Pierce expansions and continued fraction expansionsAn elliptic deformation of continued fractionsMotivic generating functions and $L$-derivatives of cohomological automorphic representationsLocal vanishing density of order $1$ and Divisor momentsMultivariate Pellarin $L$-values on algebraic curvesA Goldbach-Type Problem for the Unitary M\"obius FunctionOn the error term in Gauss's mean value formulas for class numbersTrivial solutions in Generalized Fermat equationsRestricted Quantum unique ergodicity under Generalized Lindel\"of conjectureA quantitative two-interval criterion for the Riemann hypothesisOn the lower bound for the $L^1$ norm of Liouville exponential sums. IINew lower bounds for even and odd values of the partition functionDiophantine definitions of nonsplitting for central simple algebras over global fieldsOn mod p Hecke algebras of abstract p-adic automorphic formsOn Rankin Invariants of Ideal LatticesStatistics of centralizers of integer matricesNew families of maximal curves not covered by the Hermitian curve and their cyclic automorphism groupsOn quantitative aspects of ideal membership certificate and GCD inequality for polynomials evaluated at almost unitsSmooth approximations to character sums and zeta sumsRevisiting the conjectures of Shapiro and Schanuel2-Selmer in arithmetic progressionsMonotonicity of Erd\H{o}s sumsRanks of fibers in random elliptic surfacesA rank-zero $2$-converse to the Gross--Zagier and Kolyvagin theorem for elliptic curves with abelian two-division fieldOn the $\Delta$-primitive squares conjecture$C_{\st}$-conjecture for compactly supported pro-\'etale cohomologySimple algebraic groups with good reduction, the genus problem, and unramified cohomologyAn Analytic Evaluation of Euler Sharp Sum...

密な群と局所場上の幾何学 - 2026/11/9の論文22本

37 min

arXiv math.NTの新着論文22本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-09/ Composite witness sieves, Kneser--Plancherel containers, and the exponent $5/7$ for the Erd\H{o}s--Straus conjectureBurgess' bounds with prime moduliJoint Approximation and the Mixed-Prime Character GroupAn Elementary Proof of the Binary Goldbach ConjectureThe existence of small defining polynomials for number fields, IICampana points on quadrics with hyperplane boundaryElliptic units, derived Heegner classes and the p-adic Birch and Swinnerton-Dyer quotient of CM elliptic curves of rank twoBounded Ratios of Best Approximations: Sharp Bounds and Spectra of Diophantine ExponentsRoot sharing and $2$-adic interpolation for Legendre polynomialsThe exceptional set of Goldbach numbers among polynomial valuesCurves with absolutely irreducible Tate modules over $p$-adic fieldsPermutation polynomials from quadratic and linear formsOn a Problem of Gordon and Hughes: The 11-adic Properties of Meromorphic Modular Functions on $\mathrm{X}_0(22)$Euler trace congruences over local fieldsHarper's beyond square-root conjecture for random matricesMellin Transform formulas for special values of Goss $L$-functionsCounting Finite Maps through Functional Digraphs and FibersA counterexample to Manin's Conjecture for almost Fano varietiesZariski dense hyperbolic 3-manifold groups in $\mathrm{SL}(4,\mathbb{Z})$Cuspidal sections for varieties of arbitrary dimensionOne complex metric and geometric adelic nefnessSupercuspidal and elliptic densities for reductive groups over non-archimedean local fields

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零点とコードと曲面 - 2026/11/11の論文34本

1 hr 4 min

arXiv math.NTの新着論文34本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-11/ The uncertainty operator, the Weil ground state and the zeros of zeta: a numerical study and conditional positivity of the Weil quadratic formThe $\mathbb Q$-gonality of $X_1(42)$ is $12$Bounding the security of the Bromberg-Shpilrain-Vdovina hash functionA counterexample to the Erd\H{o}s--Mahler conjectureA Threshold-Crossing Condition for the Least Colossally Abundant Counterexample to Robin's InequalityOn the equidistribution of eigenfunctions of higher dimensional cat maps modulo prime powersPeriods and CM motives of abelian typeDiophantine approximation with prime denominators in short intervalsA Moment Proof of the Hollman-Xiang Conjectures on Kloosterman PolynomialsWhen do all iterates of $x^2 + a$ have maximal Galois group?Explicit plane models for all Galois quotients of the Hermitian curveA generalized Vojta-R\'emond inequality over adelic curvesAsymptotically good codes from Siegel modular varietiesSun's conjecture on a certain ternary quadratic formA complete classification of permutation binomials of the form $X^r(X^{2(q-1)}+a)$ over finite fieldsThe exponent $3/4$ for the exceptional sets of the equations $K/n=1/x+1/y+1/z$A Complete Classification of Maximal Hyperelliptic Curves Related to Chebyshev PolynomialsCounting Rational Points on Cayley's Cubic SurfaceDivisor Folding and Finite-Group Trace ObstructionsThe distribution of small gaps between zeros of the Riemann zeta functionZeros of Katz's p-adic Eisenstein series E2Cyclically covering subspaces and additive perfect codesA cyclotomic Artin-Tate formula and sphere packing for K3 surfacesNonnegative weak tilings and the Coven-Meyerowitz condition (T2)Non-abelian $p$-adic Hodge theory and stacksDavenport Constants of High-Dimensional Integer SetsParabolic induction and pullback of perverse sheaves on Vogan varietiesThe zero-sum constant $\mathsf{s}_p^*$ and inverse problemInte...

L値とモジュラー形式とランダム代数 - 2026/11/10の論文56本

1 hr 39 min

arXiv math.NTの新着論文56本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-10/ A recursion relation for the coefficients of Swinnerton-Dyer type polynomialsA singular homeomorphism between Pierce expansions and continued fraction expansionsAn elliptic deformation of continued fractionsMotivic generating functions and $L$-derivatives of cohomological automorphic representationsLocal vanishing density of order $1$ and Divisor momentsMultivariate Pellarin $L$-values on algebraic curvesA Goldbach-Type Problem for the Unitary M\"obius FunctionOn the error term in Gauss's mean value formulas for class numbersTrivial solutions in Generalized Fermat equationsRestricted Quantum unique ergodicity under Generalized Lindel\"of conjectureA quantitative two-interval criterion for the Riemann hypothesisOn the lower bound for the $L^1$ norm of Liouville exponential sums. IINew lower bounds for even and odd values of the partition functionDiophantine definitions of nonsplitting for central simple algebras over global fieldsOn mod p Hecke algebras of abstract p-adic automorphic formsOn Rankin Invariants of Ideal LatticesStatistics of centralizers of integer matricesNew families of maximal curves not covered by the Hermitian curve and their cyclic automorphism groupsOn quantitative aspects of ideal membership certificate and GCD inequality for polynomials evaluated at almost unitsSmooth approximations to character sums and zeta sumsRevisiting the conjectures of Shapiro and Schanuel2-Selmer in arithmetic progressionsMonotonicity of Erd\H{o}s sumsRanks of fibers in random elliptic surfacesA rank-zero $2$-converse to the Gross--Zagier and Kolyvagin theorem for elliptic curves with abelian two-division fieldOn the $\Delta$-primitive squares conjecture$C_{\st}$-conjecture for compactly supported pro-\'etale cohomologySimple algebraic groups with good reduction, the genus problem, and unramified cohomologyAn Analytic Evaluation of Euler Sharp Sum...

密な群と局所場上の幾何学 - 2026/11/9の論文22本

37 min

arXiv math.NTの新着論文22本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-09/ Composite witness sieves, Kneser--Plancherel containers, and the exponent $5/7$ for the Erd\H{o}s--Straus conjectureBurgess' bounds with prime moduliJoint Approximation and the Mixed-Prime Character GroupAn Elementary Proof of the Binary Goldbach ConjectureThe existence of small defining polynomials for number fields, IICampana points on quadrics with hyperplane boundaryElliptic units, derived Heegner classes and the p-adic Birch and Swinnerton-Dyer quotient of CM elliptic curves of rank twoBounded Ratios of Best Approximations: Sharp Bounds and Spectra of Diophantine ExponentsRoot sharing and $2$-adic interpolation for Legendre polynomialsThe exceptional set of Goldbach numbers among polynomial valuesCurves with absolutely irreducible Tate modules over $p$-adic fieldsPermutation polynomials from quadratic and linear formsOn a Problem of Gordon and Hughes: The 11-adic Properties of Meromorphic Modular Functions on $\mathrm{X}_0(22)$Euler trace congruences over local fieldsHarper's beyond square-root conjecture for random matricesMellin Transform formulas for special values of Goss $L$-functionsCounting Finite Maps through Functional Digraphs and FibersA counterexample to Manin's Conjecture for almost Fano varietiesZariski dense hyperbolic 3-manifold groups in $\mathrm{SL}(4,\mathbb{Z})$Cuspidal sections for varieties of arbitrary dimensionOne complex metric and geometric adelic nefnessSupercuspidal and elliptic densities for reductive groups over non-archimedean local fields

曲線と曲面における算術的構造 - 2026/11/6の論文28本

52 min

arXiv math.NTの新着論文28本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-06/ Explicit bounds for the number of solutions to Roth-type inequalities over adelic curvesMetallic Circles: Concyclic Tangency Points of Ford Circles over $k$-Fibonacci QuotientsMahler's Problem on Liouville Numbers II. Rational MapsOn Amoebas and the Arithmetic Rigidity of the Mahler MeasureFields Generated by a Single Point on Elliptic CurvesOn explicit units in a family of cubic fields and the arithmetic of curves arising from powers of these unitsPeriodic counting, carry synchronization, and primes in nonstandard numeration systemsOn a problem due to Erd\H{o}s concerning $w_1(n)$Multivariable Congruence Jumping: Periodic States, Integral Realizations, and DescentA Hypergeometric RM Surface: Integral Monodromy and Level-11 CoversThe minimal excludant and the least $r$-gaps of $\ell$-regular partitionsTowards a twistless converse theoremOn Sufficient Conditions for Rank Zero in Families of Elliptic CurvesOverholonomicity of Overconvergent $F$-isocrystals over Laurent Series FieldsArithmetic theta products and doubling at arbitrary levelDensity and holes of the visible points in certain cut-and-project sets$p$-parity conjecture for Panchishkin Galois representationsPointless K3 surfaces over finite fieldsAn extremal unimodular lattice of rank 37Gaps in the Most Frequent Sizes of Integer SumsetsBrauer groups of generalised Markoff surfacesCombinatorics of noncommutative harmonic oscillator determinantAnti-ribbon shaped Young diagram decompositionThe parity of the number of missing integers in partitionsThe Calkin--Wilf problems on $\ell$-ary partition functionsCounting multigeodesics and the Selberg-Delange methodFermat quotients with CM Jacobians and trivial automorphism groupSteinberg module and top-dimensional cohomology for arithmetic Chevalley groups

表現論とディオファントスとqゼータ値 - 2026/11/5の論文29本

51 min

arXiv math.NTの新着論文29本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-05/ A normalization issue in a transmitted form of Bloch's diamond formula: anti-invariant subgroup versus regulator quotientLow moments of sums of extended Rademacher random multiplicative functionsOn the existence of nonadmissible irreducible smooth representations of $p$-adic $\mathrm{GL}_n$Partitions with designated summands: $k$-tuples and their congruencesOrbit Transversality for Projective SpaceDiophantine definability from addition and divisibility over rings of $S$-integersSecond moment of incomplete Eisenstein series revisitedCollision Parameters in Higher-Dimensional Families of PolynomialsTwisted Diophantine approximation: asymptotic and uniform resultsA Rankin-Selberg Integral for $SU_{2,2}$Maximal Unipotent Monodromy and $p$-adic Eigenvalue FormulasThe enhanced polylogarithm conjecture in weight two for imaginary quadratic fieldsPoissonian Pair Correlation and Discrepancy RatesThe Minimal excludant of $\ell$-regular partitionA Galois-type Springer theorem for hermitian and generalized quadratic formsRational Torsion and Ramification Constraints on Odd Superelliptic JacobiansCertified Collision Exclusion and an Unconditional Upper Bound $\LambdaHopf-Galois Structures on Extensions Arising from Division Points on Elliptic CurvesMultiple $q$-zeta values as polynomials in partition multiplicitiesPrivate key sieves for improved attacks on RSAImproved deterministic integer factorization by quadratic-image sievingUnit fraction representations using shifted Golomb primesAn Asymptotic for E. P. Stein NumbersExact $3$-Adic Periods of Symmetric Dellac Numbers and Their Polynomial ExtensionsNon-admissible smooth irreducible representations of $\mathrm{GL}_2(F)$ for totally ramified extensions $F/\mathbb{Q}_p$PCF All The Way DownArthur packets for $\mathrm{G}_2$ over $p$-adic fieldsProof of two conjectures on the log-concavity of partition ranks a...

整数方程式と楕円曲線と分割 - 2026/11/4の論文24本

42 min

arXiv math.NTの新着論文24本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-04/ A generalization of the Dirichlet approximation theorem for affine actions on the real lineClassification of torsion of elliptic curves over sextic fieldsSome instances of modularity for residually reducible representations in the mixed caseRamanujan-type congruences for the smallest parts functionRational points on loxodromic K3 surfaces and complex dynamicsOn integers $n$ relatively prime to $\lfloor \alpha n^2\rfloor$The smallest-parts function and elliptic curvesFinding Integer Roots of Polynomials in Nearly Optimal TimeCounting irreducible skew polynomials $x^{2n}+ax^n+1$Inverse powers and 2-adic properties of binary 3 x 3 matrices associated with the Tribonacci sequenceAsymptotics for partitions over the Fibonacci numbers and related sequences, IIOn the Diophantine equation $Cx^2+p_1^{2m_1}p_2^{2m_2}\cdots p_k^{2m_k}=y^q$Almost primes in short intervals and averages of long Dirichlet polynomial approximations to $(\zeta'/\zeta)^{k}$On partitions with bounded multiplicity restrictions on even parts and with the largest part being oddDivisibility Properties of Odd Part and Even Part Sums in Cubic PartitionsOn the van der Corput property for cubesSumming over Seifert Manifolds in Narain Ensemble AveragesOn the Irreducibility of Locally Analytic Vectors in Certain Banach Representations of $D^\times$Good slopes, congruence preservation, and gaps over residue ringsPolynomial configurations and pointwise averages along Piatetski--Shapiro primesAdditive energy, Freiman's lemma, and an edge-isoperimetric problem on the boolean cubeRelative Tate-Shafarevich kernel of a reductive group over a global fieldHecke Relations from Self-DualityOn the $abc$ conjecture

構造と分布とL関数とディオファントス - 2026/11/3の論文87本

2 hr 32 min

arXiv math.NTの新着論文87本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-03/ Cuspidal sheaves on the stack of L-parametersPorosity in Diophantine approximationOn the Distribution of Prime Squares and Its ApplicationsA power-saving asymptotic for a M\"obius-weighted GCD quadratic formThe distribution of $\alpha\pi$ modulo one in $\Fq(T)$: beyond Matom\"aki's exponentCyclotomic polynomials with trinomial irreducible factors over finite fieldsOn Certain Congruences for Partition $k$-Tuples with $5$-CoresPartition statistics and universal mixed mock modular formsTwisting-free converse theorems for $\Gamma_0(32)$ and $\Gamma_0(36)$On Ramanujan's cubic continued fraction, IIThe covering radius of the first-order Reed-Muller code in nine variables is 242An exhaustion-aware product moment and zero-free half-planes for Hecke L-functionsTwo-point Pad\'e approximation and patterns in continued fractions for $(F_{n+1}/F_n)^k$Uniform cubic bounds for irrational values of the dilogarithmOn Wagstaff primes in the $k$-Pell number sequenceFermat curves and explicit class field theory for real quadratic number fieldsEntanglement for elliptic curve group ordersSmall-LCM Distinct Covering Systems via Segmented Local SearchA secondary term in the first moment of primitive cubic Dirichlet L-functionsImproved first moments of primitive quartic and sextic Dirichlet $L$-functionsAdelic Galois representations are maximal for almost all Drinfeld modulesA solution to the Erd\H{o}s-S\'{a}rk\"{o}zy product-density problemA Counterexample to Wooley's $L^1$ Question for Beatty SequencesSmooth numbers in simultaneous arithmetic progressionsCounting Nilpotent Galois extensions with prescribed genus numberA new upper bound for the irrationality exponent of $\zeta(5)$Irrationality measures for $\Gamma(1/4)$ and $\Gamma(1/3)$Inhomogeneous Fiber Refinement of Gallagher's TheoremGroups of Prime UnitsFinite Cotangent Power Sums Weighted by Additive Characters...

モジュラ性とスペクトル理論 - 2026/11/2の論文27本

47 min

arXiv math.NTの新着論文27本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-11-02/ A law of the iterated logarithm for random multiplicative functions on integers with a large prime factorIntegral Brauer--Manin Obstruction for Fermat Near MissesA Local Fourier-Transform Proof of Offen's Spherical Transfer TheoremErd\H{o}s--Straus Conjecture: Modular Inversion in Mordell ClassesClusters of primes revisitedA spectral theory of zeta functions of function fieldsWeil Operators and Remainders of Anderson Generating Functions over a Punctured Projective LinePositive Values of Inhomogeneous Quadratic Forms of Type (1, 4): The Constant \Gamma_{1,4} = 8Vector Valued Katok-Sarnak FormulasKloosterman Sums and Pl\"ucker Height Zeta FunctionsPrimes and the M\"obius function over quadratic polynomialsTwisted second moments of Dirichlet $L$-functions with applications to weighted one-level densityIrrationality of values of $L$-functions for real Dirichlet charactersOn sign patterns of Fourier coefficients of theta quotientsIterated toric descent obstruction and homogeneous spaces over geometric global fieldsJoint universality of the Riemann zeta-function with arbitrary real shift parametersEstimates of Lucas series and expansions in non-integer basesOn the modularity of residually reducible Galois representations of rank 2A conjecture on Galois groups and large fieldsCentral values of additive twists of automorphic $L$-seriesSpectral Beurling-Selberg Approximation and Applications to Effective Motivic Chebotarev-Sato-Tate EstimatesOn the Iwasawa invariants of admissible quadratic twists of elliptic curves at ordinary Eisenstein primesDescent and Decomposability of Algebras of Exponent 2 in characteristic 2Four runners that are barely lonelyA Diophantine generalization of Fourier's irrationality trickThe complexity of tiltingLimit theorems for cuspidal orbits on Fuchsian groups

幾何構造と数論的解析 - 2026/10/30の論文61本

2 hr 5 min

arXiv math.NTの新着論文61本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-30/ The View-Obstruction Problem for Spheres in Dimensions Six and SevenJacob's ladders and wander from Hardy-Littlewood integral (1918) to the $\zeta$-Platonic cube form of equivalent of the Fermat-Wiles theoremOn the convexity of the fundamental domain of binary cyclotomic formsNovel properties of polynomialsA complete classification of minimal value set polynomialsVan der Waerden's Problem for Cubic SurfacesA Kohnen-Zagier Formula in Level 1Determining norm-Euclidean complex cubic fieldsGeometric properties of the analytic Emerton-Gee stackA note on a problem of Ma and ChenThe Borisov--Nuer conjecture and root decompositions in even unimodular Lorentzian latticesLifting mod $p$ Galois representations over local fieldsRepresentations and $n$-universality of hermitian lattices over local and number fieldsAn asymptotic Jensen-Polya criterion for GRHSerre's conjectures for $\Q(\sqrt{13})$Reciprocity formulas for generalized Dedekind character sumsCA2 numbers and the Riemann hypothesis: a numerical investigation of Ramanujan's inequalitiesFree modules of vector-valued modular forms and applications to Jacobi formsCentres of mass, Steiner's theorem, and equations of Erd\H{o}s-Moser typeThe trace distribution of $r$-primitive $k$-normal elements of finite fieldsAn introduction to the strategy of transcendence proofsOn short averages of the Fibonacci partition functionRational points of exact period three for the quadratic familyMoments of characteristic polynomials at random matrix Gram pointsLow-rank matrices with three prescribed off-diagonal values over $\mathbb{F}_p$Least common multiples of polynomial values: averaging, ray classes, and Galois statisticsVanishing near the virtual cohomological dimension of $\mathrm{SL}_n(\mathbb Z)$Hilbertian Fields and Profinite Iterated Monodromy Groups Over Transcendental Elements with Specializations of Infini...

L関数と$p$進構造と幾何学的解析 - 2026/10/28の論文41本

1 hr 22 min

arXiv math.NTの新着論文41本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-28/ Counting Markov triples and simple geodesicsUniform local models of quasi-unipotent $p$-adic differential equationsHankel determinants for the $(n+2)$-shifted $q$-metallic numbersComputations in weight 3 of higher Bloch groupsInfinite families and sporadic solutions of the equation $\varphi(n)=c+\alpha\sum_{p\mid n}\varphi(p)$Retriangular numbers and affine maps between polygonal numbersPointwise to global good reduction problemsGross--Prasad conjecture in geometric LanglandsMetric Diophantine approximation with primes on irrational linesExact Generic Exponents of Approximation for the Action of the Integral Special Linear Group on the TorusMoment representations for generalized Lehmer polynomialsEffective Chebotarev-Sato-Tate distribution for Abelian varieties with applicationsArchimedean zeta integrals on $ {\rm SO}_{2n} \times {\rm GL}_n$ and $ {\rm Sp}_{2n} \times {\rm GL}_n $Resolvent Components of Completely Normal Elements and the Morgan-Mullen ConjectureSquare-root logarithmic bounds for the arithmetic complexity of factorial multiplesOn the interpolation property of Kupferer's Lubin-Tate regulator mapsArithmetic Poisson summation formulasOn extended interpolation properties of the Katz $p$-adic $L$-functionFinite Fields: Root Sets, Frobenius, and Algebraic StructureDensity and Defect Distribution of Reduced Ideals Missed by the Reduction Algorithm in Real Quadratic FieldsLarge values of Hardy's Function from the Selberg classNear-quadratic sum-product estimates in fixed number fieldsFactorization of Elliptic Divisibility Sequences via Modular CurvesExplicit Serre weights for modular Galois representations of $U(2)$Universality Criterion Sets for Definite Quadratic Lattices over Polynomial RingsOn $p$-Adic Valuation Trees Arising from Laplace Transform of Fibonacci PolynomialsA zero-density estimate for the symmetric square $L$-function...

構造と数論と幾何学の探求 - 2026/10/27の論文53本

1 hr 47 min

arXiv math.NTの新着論文53本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-27/ A Sharp Distributional Lower Bound for Planar DiscrepancyOn the unit group of some triquadratic fieldsTwo parametric $q$-supercongruences from Andrews' multi-series transformationOn the evenness of coefficients of modular formsA secondary term in the first moment of cubic $L$-functions over function fieldsLocal obstructions and certified computations for perfect powers in power sumsHeight growth of rational self-mapsSquarefree Values of Random PolynomialsOn Lehmer's ProblemZassenhaus Filtration and Ihara ConstantsJoint Extension Field Point Counts for Superelliptic CurvesExploring topological features of a complex network of prime factors and composite numbersExplicit Coleman integration over finite extensions of $\mathbb{Q}_p$Finite-sum Identities and Supercongruences for Cubes of Catalan NumbersCross numbers and the characterization of finite abelian groups by length setsThree Quadratic Recurrences Modulo 3: What We Can Prove and What We Can GuessOn real biquadratic number fields for which the $2$-Iwasawa module has rank $3$A symmetric extension of Zhao's series for $\zeta(5)$Frangible prime gapsResults for distinct covering systems with a prime minimum modulus $q \ge 11$Admissible sets of integers in imaginary quadratic fields of class number 1Finiteness theorems for trace Euclidean quadratic lattices over totally real number fieldsGeometric progressions in distance sets in odd dimensions over prime fieldsThe Family $X_{qp^s}$ for Distinct Primes $q,p$ in Connection with Carmichael's Totient ConjectureHartl's dictionary and a transcendence characterization of equicharacteristic local shtukas with complex multiplicationDynamical Chowla conjecture for polynomials of several variablesCounting Integral Matrices with Given Cubic Characteristic PolynomialNon-liftability of the field of norms of the $p$-adic false Tate curve extensionOn almost perf...

シンタニと二次形式と有限体上の算術 - 2026/10/26の論文22本

42 min

arXiv math.NTの新着論文22本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-26/ Biases in gaps between zeros of Dirichlet L-functionsDivisor Sums with Spacing ConstraintsQuantitative nodal domain count for Maass formsOn Parameterization of Some Problems in Number TheoryElliptic curve rank growth in multi-quadratic extensionsTrivial Iwasawa modules and arithmetic linking numbersAn explicit bound on $|\zeta_K(1+it)|$A Sharp Upper Bound for the Frobenius NumberValue-distribution of Euler--Zagier type multiple zeta-functions with identical arguments on the critical linePrime Numbers of the Form $24m+1$ and Erd\"{o}s-Straus ConjectureShintani Cocycle Decomposition of Topological Polylogarithms for Totally Real FieldsBinary Quadratic Forms, Shintani Lifts, and Twisted L-ValuesThe limiting zero counting measure for Eisenstein seriesHausdorff dimension of canonical height spectraThe Hardy--Littlewood asymptotic for primes $p$ and $p+4$ from a uniform zeta-ratios conjectureA genus-two spectral curve of the Riemann $\Xi$-function: Real Structure and Certified Arithmetic Separation of PeriodsSpectral convergence associated with Weil's quadratic formTraces of Green's functions on $\mathbb{H}^q$ over point-hypersurface pairsRational Points on Affine Varieties over Finite Fields and Polygonal Number SequencesPower Sum Varieties over Finite FieldsPartial rigidity and q-additive functionsDeterministic Root-Finding over Finite Fields with Elliptic Curves

幾何と周期と零点の解析 - 2026/10/23の論文25本

50 min

arXiv math.NTの新着論文25本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-23/ Simultaneous popular polynomial differences in higher dimensionsAn explicit elementary proof of no Landau--Siegel zerosNorm-Euclideanity in cyclic fieldsOn the Open Problem in the 2023 Simon Marais Mathematics CompetitionAspects of quadratic Chabauty via modular formsComplete Determination of the Gallai--van der Waerden Number \(\mathrm{GW}(r;3,3)\)OpenAI partially disproves Littlewood's 1961 $L^\alpha$-flat theoremThe exponent $1/4$ in three complexity bounds: integer bases, continued fractions, and the $(3/2)^n$ steering wordIrrationality Exponents of Real CM Elliptic Periods and Powers of the Lemniscate PeriodOn the arithmetic Siegel--Weil formula for orthogonal Shimura varieties over a general totally real fieldLandau-Siegel zeros over a base field and effective Brauer-SiegelNonvanishing of 2-primary Kolyvagin classes via simultaneous quadratic twistsDenominators of Hodge integrals and Minkowski numbersRelative Hitchin fibrations and endoscopy for Unitary Friedberg--Jacquet varieties$\SL_3$ dual pairsAsymptotics of local height pairing without Hodge conjectureA general quantified Wiener-Ikehara theoremExact Archimedean Flicker--Rallis Periods on Cohomological Minimal $K$-TypesNonexistence of Constant Congruences for the Cumulative Partition FunctionOpen dynamics with a moving hole: inhomogeneous IFS and exponential separation conditionLog blow-ups and global resolutions in rigid geometryCohomology of integral structure sheaves for open varietiesLocal heights for nef toric compactified divisorsDeep holes of full-length Reed--Solomon codes: uniform bounds and exact classificationsLanglands-Shahidi gamma factors and local transfer in families

整数値と集合和と群の構造 - 2026/10/22の論文35本

1 hr 11 min

arXiv math.NTの新着論文35本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-22/ An Asymptotic for Non-Wieferich NumbersA Counterexample to the Eventual Stability ConjectureSch\"affer's conjecture for even $k \le 42$A quaternary Diophantine inequality with prime numbers of a special form (II)A relative Schinzel-Zassenhaus bound for the polynomial $T^2 - 1$Short sums of the M\"obius function over function fieldsSubset sums of power values over Galois ringsOn a conjecture of VelaniHecke Orbits on Globally Drinfeld-Uniformized Shimura Varieties Are $p$-adically Nowhere DenseThe Octonionic Rational Wave Numbers: Non-Associative Sequence Algebras, Moufang Loops, and Exceptional $G_2$ SymmetriesZeros of quadratic Dirichlet $L$-functionsConstruction of Galois modules describing ideal class groups and applications to Iwasawa theoryMixed sums of infinite multiple zeta-star values with restricted indicesStatistics of entries of matrices from the general linear group over a finite fieldIdeal class groups of certain real quadratic number fields and factorizations of values of certain quadratic polynomialsComputing Theta Characteristics and their Galois action on general curves of moderate genusThe exceptional set of Goldbach numbers within the set of squaresResidue Sums Modulo Products of Two Distinct Odd PrimesPerturbing the Conway sequenceOn the Gauss sphere problemSharp spherical $L^p\to L^4$ extension estimates over finite fields in odd dimensionsInteger symplectic matrices in expanding boxesIntegral trace forms of cyclic number fields without tamenessOn the notion of reasonable functions in Cohen--Lenstra type heuristicsSquarefree values of random polynomials are Gaussian mixturesA Sharp Bound for Additive ComplementsZeros of $E_2$, quasi-periods, and Schwarz mapsSupport periods of polynomials and support-primitive decomposition of constacyclic codes over Galois ringsLocal Gan-Gross-Prasad conjecture for unitary groups: Trace form...

L関数とコードと割った集合 - 2026/10/21の論文35本

1 hr 7 min

arXiv math.NTの新着論文35本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-21/ Galois Groups of Shifted Exponential PolynomialsClass polynomial obstructions to canonical congruences for the smallest parts functionSmall sums of roots of unity: polylogarithmic exceptional sets and conditional separationUpper Bounds on the de Bruijn-Newman constant for Dirichlet $L$-functions with primitive real-valued charactersThe Projective Reed-Muller Code from Quartic Curves in the Projective PlaneQuantum Variance for Hecke--Maass Cusp Forms on the Vertical GeodesicBowen--Franks groups and minus class groups of imaginary abelian fieldsNon-vanishing of central values of angular Hecke $L$-functionsOn a Notion of Density Related to Restricted Diophantine ApproximationAn Equivariant Main Conjecture for Branched $\mathbb Z_p$-Towers of Finite Graphs and ApplicationsSmall values of the Riemann zeta-function near the critical lineA determinant formula for multiple harmonic sums and their linear independenceDense Sets with Prescribed Difference Representation FunctionsNew Directions in IrrationalityWeyl Bounds for $\operatorname{GL}_2\times \operatorname{GL}_2$ Rankin--Selberg $L$-functions via Short Spectral MomentsPrimes in short intervals assuming the Riemann hypothesisPost-quantum commutative group actions from oriented superspecial abelian varietiesTheta RelationsSEAC from EAC modulo Schanuel: reduction to algebraic exponentialsUncountably many settled elements are never Frobenius elementsOn the average of class numbers of indefinite binary quadratic formsIrrationality exponents of logarithmic numbers: Values, quotients, and graded approximationSimultaneous visibility in cut-and-project setsEuler systems for self-dual Hecke characters over biquadratic fields with applicationsSimultaneous popular differences for polynomial and linear progressions in finite fieldsA necessary condition for a Romanoff type theoremA Joint Local Limit Theorem fo...

L関数とモジュラー形式とp進表現 - 2026/10/20の論文60本

1 hr 38 min

arXiv math.NTの新着論文60本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-20/ Ramanujan Conjecture and Riemann Hypothesis for the unitary groups over function fieldsGaps for PLRS with zero coefficientsDihedral fields with Bloch lattice index five and quadratic subfield Q(i)Recovering Dirichlet coefficients from even samplesDiamond Maximal Operators: Classification, Moduli, and Oscillation EnvelopesOn the Ramanujan-Ligozat modular unitThe exact Euclidean window of $\mathbb{Z}[\sqrt{14}]$Markoff spectra of Hecke groupsPillai's equation between k-generalized Pell numbers and Tribonacci numbersStevens' Approach to Kloosterman Sums on Split GroupsHuman Exposition of Claude's 2/3 Theorem on the zeros of zetaInverse trigonometric and hyperbolic identities,series and products for Lucas sequencesOn reducible $\ell$-torsion representations of Picard curvesDouble shuffle and naive duality for multiple Dirichlet seriesAll totally real abelian number fields of class number one are EuclideanLarge values of derivatives of quadratic Dirichlet $L$-functionsThe 3-adic Steinberg block and a categorical 3-adic local Langlands correspondence for $\text{GL}_2(\mathbb{Q}_3)$Graded Structures of $v$-adic Carlitz Multiple Polylogarithms and $v$-adic Multiple Zeta ValuesA sharp lower bound for $h$-fold restricted sumsets of integersCovering finite fields by translates of multiplicative subgroupsLucas' Theorem modulo $p^n$ via Harmonic sums$2$-adic Representations of Elliptic Curves over $\mathbb{Q}_2$Mixed Tate Chabauty--Kim beyond the polylog quotientDistinctness and Algebraic Degrees of Inverted Kloosterman SumsHeights of small CM cycles on Unitary Shimura VarietiesThe factorial separation conjectureOn The Manin ConstantRational Points on Drinfeld Modular Curves of Prime LevelFrobenius Profiles of Polynomial-Multiple MRD CodesA Fourier expansion principle for coherent cohomology of powers of Tate curvesAsymptotic low slopes of toric exponential...

モジュラー形式とガロア群の解析 - 2026/10/19の論文34本

1 hr 8 min

arXiv math.NTの新着論文34本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-19/ Space-filling curves and small-ball probabilities for the Kloosterman processA Non-Split Motohashi Formula for Toric Periods over Number FieldsDensity Bounds in Hua's Theorem for Prime SquaresGalois Groups of Trinomials with Small CoefficientsPoisson-Dirichlet statistics for the log-modulus of the Riemann zeta function on expanding intervals near the critical lineMetric Poissonian Pair Correlation Property Part 2: The Case \(n\log n\)Metric Poissonian Pair Correlation Property Part 1: The Case \(n+\log n\)Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta FunctionImproved explicit Burgess-strength bounds for composite moduliArithmeticity of critical $L$-values for Hilbert-Siegel modular forms in the left half plane and $s = 1$Zagier's 2-3-2 formula for multiple Eisenstein seriesMinimal asymptotic \(g\)-adic bases from arbitrary partitionsA $\mathrm{GL}_3$ level analog of Selberg's result for $S(t)$Note on the largest prime factors of consecutive integersImproved $L^p$ maximal estimates for higher-degree Weyl sumsMahler Method and Vanishing TheoremMore than 8/9 zeros of the Riemann zeta function are simple or on the critical lineLifting mod $p^n$ Galois representationsOn a series related to the M\"obius functionFourier dimension for exactly approximable matricesCuspidal Class Number Formulae for Intermediate Modular Curves of Prime LevelConfluence relations, Hoffman basis over \mathbb{Z}_{(2)}, and the Deligne--Drinfeld conjectureThe distribution of $\alpha p$ modulo one in real quadratic function fieldsNear optimal gap in the Lonely Runner ConjectureA duality principle for the neighbourhood of manifolds and applications to counting rational points near curvesA $p$-adic Riemann--Hilbert correspondence over Robba ringsA Simple Proof of I. Chowla's Theorem on Addition of Residue ClassesPresenta...

L関数と指数和とガロア環 - 2026/10/16の論文39本

1 hr 16 min

arXiv math.NTの新着論文39本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-16/ 86 unknowns for Hilbert's tenth problem over the rationalsMixed moment and joint non-vanishing of $\mathrm{GL}(3)\times\mathrm{GL}(1)$ and $\mathrm{GL}(1)$ $L$-functionsEhrhart Polynomials of Triangles in $\mathbb{R}^3$On the Diophantine equation $X^2+p^m=p_1^{n_1}p_2^{n_2}$CM Elliptic Analogue of the Coleman--Ihara FormulaA simpler proof that there are no Landau--Siegel zerosOptimal Reduced Representatives of Quadratic APN Permutations in Odd DimensionExplicit reduced APN permutations: ramification and optimal Galois-ring liftsNon-vanishing mod $p$ of derived Hecke algebras of multiplicative groups over number fields, IIModularity criteria for multiple Eisenstein seriesOn the dimension conjecture for global Galois deformation rings in characteristic twoSmoothness of Shortest Isogenies to Frobenius ConjugatesImaginary quadratic fields of class number at most 2000Frey-Mazur theorem for semistable elliptic curves over function fieldsLocal Tate duality for syntomic cohomology in positive characteristicA prime plus a square: A conditional 11/20 upper boundA New Bound for the Gauss Circle ProblemA number field extension of Ramanujan's identity and its integral representation via the generalized Riemann $\Xi$-functionTwisted Artin-Schreier Theory I: $(C_p \rtimes C_{p-1})$-extensions of local function fieldsIsaac's Condition (TU) is falseA variation on local trilinear formAn introduction to algebraic groupsOn the Sampling of Certain Dirichlet and Prime Sums at Gram Points and their ViscosityClassification of vanishing fusion rings of rank fourEkedahl-Oort strata with a superspecial factor in unitary Shimura varietiesLogarithmic exponential sums with multiplicative coefficientsThe discrete second moment of the Riemann zeta-function along powers of Gram pointsVariation of Shafarevich-Tate groups in Hida familiesAutomorphic Dirac Operators and an Analog...

代数幾何と算術的構造の解析 - 2026/10/15の論文39本

1 hr 18 min

arXiv math.NTの新着論文39本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-15/ On digit-appending walks along linear recurrencesLarge value estimates for Dirichlet polynomials and trilinear sums over short intervalsOrthogonality relation between $GL(3)$ coefficients and additive characters with linear and non-linear phasesSome Bounds on the Lehmer IndexElliptic curves attached to Jacobians with imaginary multiplicationA new way integral for the $n$-fold cover of $SL_2$An algebro-geometric approach to profinite iterated monodromy groupsA Bounded-Defect Construction for the Mondrian Art ProblemReductions of Galois representations of slope $2$Zero-cycles and Brauer groups on certain Enriques surfacesTernary polynomial relations and periods of cusp formsShapes of tame abelian number fieldsA folklore conjecture on multiplicative exponential sumsArithmetic Visibility in Polygons: Curved Sight in the Art GalleryOn a problem on partitions into distinct primesThe Density and Quantitative Upper Bound of Integers Not Expressible as the Sum of a Prime and a Zumkeller NumberOn the Erd\H{o}s--Odlyzko--S\'ark\"ozy conjecture for prime-power moduliDivisibility Estimates for Gaussian Norms and Almost-Prime Orders of a CM Elliptic CurvePrimes between 8th powers?Conguences for Odd Unimodal Sequences and a Problem of Bringmann And LovejoyIntegral Specializations of Polynomials: Hilbert Irreducibility, Coprimality, and DensityNew bounds for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ shifted convolution sumsGenus character $L$-functions of orders in quadratic function fieldsOn the Hardy--Littlewood--Chowla conjectureAn upper bound for valuations of elliptic nets at primes of bad reductionQuantitative lower bound for Pythagorean pairs in boxes of prime powersS-squareful values of binary quadratic formsGCD and ABC inequalities for abelian varieties over function fieldsUniversal norms of partially de Rham $B$-pairs and perfectness in Lubin--Tate Iwasaw...

格子とモジュラーとp進と組合せ - 2026/10/14の論文117本

3 hr 52 min

arXiv math.NTの新着論文117本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-14/ Counting quaternion extensions by multi-heightsGeometric bounds on norms of signed indecomposable integersWendt's determinant and finiteness of prime characteristics for permutation binomialsLinking numbers and special differential characters in arithmetic hyperbolic manifoldsSome applications of the quasi-Riemann hypothesis to class groups and small generators of number fieldsOn Permutations Whose Adjacent-Sum Reciprocals Sum to OneA Combinatorial Proof of Partition Identities for the Number of Distinct Part SizesUntrodden pathways in the study of partitions with parts separated by parityHigher rank elliptic sieve via CM endomorphismsCounting matrices with given characteristic polynomialA certified classical-strip comparison for the de Bruijn-Newman constantOn Berndt-Straub conjectures about zeros of generalized Ramanujan polynomialsA generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral ${}_2H_2$ summationFine structure of even Galois deformation ringsA recurrence in logarithmic M\"obius sums with coprimality conditions via Euler--MaclaurinYau's number-theoretic conjecture and sharp spectral bounds for quantum harmonic oscillatorsA sharp lower bound for the sextic large sieveSimultaneously preperiodic points and colliding orbits for families of polynomials in characteristic $p$The local structure of refined class groups in cyclotomic Iwasawa theoryRoth's theorem on weighted projective linesProofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_{2\ell-1}^{(2)}$Multidimensional Szemer\'edi Theorem for Pairwise Independent Jointly Intersective PolynomialsProof of a nonnegativity conjecture of Prellberg--StantonIntegral trace duality and the Witt filtration on Lubin--Tate spaceModuli descriptions of v-sheaf local modelsHyperelliptic curves on $K3$ surfacesHigher derivat...

幾何的構造と特殊数列 - 2026/10/12の論文36本

1 hr 12 min

arXiv math.NTの新着論文36本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-12/ On $m$-fullness in number fieldsProperness of the Cuspidal Hilbert EigenvarietyA cyclotomic gluing construction for lattice sphere packingsHankel Matrix Decompositions and Digital Sequences over Function FieldsPolynomial parametrization of $\text{SL}_2$ over global function field ringsA Rigid Analytic Curve Can Have a Dense $p$-adic OrbitA conditional bound $\Lambda\le0.13963$ for the de Bruijn--Newman constantReciprocal LCM powers and Robin's criterionReasonable bounds for Restricted Polynomial Progressions in $\mathbb F^n_p$On the Imaginary Part of $\zeta'/\zeta$Odd order cases of Chowla's averages over arbitrary rectanglesProduct and Quotient Set Dominance in Finite GroupsOn Quadric Surfaces Weighted by Arbitrary CoefficientsHecke Eigenform Product Identities for Full-Level Hilbert Modular FormsThe order types of the supports of $p$-adic algebraic Hahn seriesStieltjes constants for Hurwitz-type L-series attached to periodic arithmetic functionsTowards linear growth for biprojective hypersurfaces of small dimensionReal Fiducial Vectors Only Exist in Dimensions $d\equiv 3 \pmod{4}$On the Quantitative Bounds of Nonlinear Roth TheoremHecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$Short Recurrences and Straight-Line Programs for PrimesSharp Bounds for Limits of $N$-Point CorrelationAppell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-FunctionsRegularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of $(-1)^{\omega(n)}$On a conjecture on Romanoff type representationsOn Divisor Function Polynomials and Dirichlet SeriesOn the saturability of $p$-adic Lie groupsAn Infinite Family of Ap\'ery-like Recurrences for Euler's ConstantCovering plane curves over finite fields with linesKhintchine dichotomy for images of self-similar measures and almost random wal...

L関数と幾何と整数集合の統計 - 2026/10/9の論文52本

1 hr 47 min

arXiv math.NTの新着論文52本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-09/ The Integer Values of $\sum_{i=1}^{n}\frac{1}{\gcd(n,i)}$The structure of irreducible cuspidal eta quotientsLogarithmic moments of the Rogers Ramanujan continued fraction and odd zeta valuesMultiplicity Constants for Rough Numbers in Prime GapsFinite-radius Jensen and relative-entropy formulations of the Balazard--Saias--Yor criterionSimple and accurate approximations to Dirichlet $L$-functionsA Generalization of the Riemann Functional Equation with Three VariablesIrreducibility of Generalised Laguerre Polynomials for Large Integer ParametersClassification of the Orbits of Three Quadratic Collatz-type MapsSimultaneous non-vanishing of twists of $\mathrm{GL}_3$ and $\mathrm{GL}_1$ $L$-functionsLong intervals of consecutive composite values of polynomialsCardinalities of Jordan Diophantine sets of upper triangular integer matricesNon-degeneracy and Fibering with Applications to Diophantine ApproximationEquidistribution of number theoretic point sets in the torus and the sphere in Wasserstein metric and $L^2$ discrepancySplitting fields of complex hyperbolic groups: matrix extraction, Hermitian descent, and spectral fieldsAdditive Sums of Generalized Shifted Ternary Divisor FunctionsA note on Riemann's $R$-function and almost primesA combinatorial proof of the quadratic Gauss sumHorizontal moments of Kloosterman sums and a density version of sievesAutomorphic symbols and automorphic \emph{L}-values of GL(2) over imaginary quadratic fieldsStatistics of divisor functions over function fieldsRay class monoids for orders of number fieldsWeak and genuine A_n-formality for number fieldsInvariant Measures on Smooth Algebraic Groups over Higher Local FieldsDiscorrelation of the M\"obius function with linear phases in short intervalsNew Hoffman-type generators for alternating multiple zeta valuesA Unified Framework for $p$-adic Congruences and $p$-adic Int...

幾何学的対象と数論的解析 - 2026/10/8の論文29本

59 min

arXiv math.NTの新着論文29本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-08/ Mean Estimates for Short Polynomial Exponential Sums over PrimesConsecutive Cycle SumsMore than 83.9% of the zeros of the Riemann zeta function are distinct and more than 67.35% are simple and on the critical lineAutomorphisms of general modular curvesAffine Coordinate Subspaces and Strong Khintchine ConvergenceIdempotence in Carmichael and Giuga numbers and its application to the Agoh-Giuga conjectureOn a Digital Signature Based on Matrix Decomposition and the MinRank ProblemOn the algebraic and analytic ranks of the twin-prime elliptic curve $y^2=x(x-2)(x-p)$Regular integral models of Shimura varieties and a conjecture of PappasHigher order uniformity of the primes and cancellation of the M\"obius function in shorter intervalsPrime points on smooth hypersurfacesLinear independence of values of polylogarithms with periodic coefficients, outside the disk of convergenceMaximal volume of convex bodies avoiding random points and lacunary dilatesTranslation-invariant equations in $\mathbb{F}_p^n$ and groupsTerminal Blocks of Primes in Pisot Numeration SystemsSpacing statistics for a point scatterer on the cubic three-torusConsecutive Rankin-Cohen Bases, Full-Spark Periods, and Divisor-Tau CongruencesInvariant Primes in Lubin-Tate Space and Hovey-Strickland at Every HeightGenerating sets for maximal orders in rational quaternion algebrasImproved average and almost-all bounds for $G(n)$Irrationality exponents of logarithms of positive rational numbersIntersecting a curve in an abelian variety with multiples of another curveLocal Factors in the BSD Conjecture: A Unified Statistical ViewCocycle Relations and Elliptic Gamma ValuesMixed moments of arithmetic functions and Kloosterman sums$p$-class groups in the cyclotomic $\mathbb{Z}_p$-extension of imaginary quadratic fieldsEquivariant Unirationality of Cubic ThreefoldsMaking Every Number from 1 to N Un...

形式と数体と幾何学的構造 - 2026/10/7の論文31本

1 hr 5 min

arXiv math.NTの新着論文31本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-07/ Densities of Picard Rank Jumps for K3 Surfaces Over Global FieldsCUDA-MPQS: A GPU-Resident Self-Initializing Quadratic Sieve, and the Factorization of RSA-155On the class number of real multiquadratic fieldsThe One-Power Erd\H{o}s Conjecture for Primes $p \equiv 7 \pmod{36}$Systems of equations with elements of finitely generated groups and with linear recurrence sequencesOn eutactic formsLifting ethereal Bianchi modular formsGaps theorems for linear forms with cubic coefficientsFurther results on the paramodular Hecke algebraPrimitive normal progressions in finite fieldsA new bound for the Furstenberg--S\'ark\"ozy theorem using the van der Corput propertyCarlet's cyclic-additive conjecture for the Kasami monomialsA concise proof of the 8 case of Sylvester's conjectureThe Artin-Davenport conjecture on cubic formsThe average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integerPerfect powers with few digits and $S$-unit coefficientsPrimitive Fourier Coefficients of Hermitian Klingen-Eisenstein SeriesAlgebraic Eisenstein classes for $\mathrm{GL}_n$ with applications to the Bianchi caseGenerating and generalizing MSTD sets through Markov processesOn S\'{a}rk\"{o}zy's Local Extrema ConjecturesThe least prime with a given primitive root and a variant of the larger sieveLocal newforms, Pa\v{s}k\={u}nas-Stevens Whittaker functions, and explicit test vectors for $\mathrm{GL}(n)\times \mathrm{GL}(n)$New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutationsNew algebraic points on covers of elliptic curvesMixing of the BCZ MapHigher additive energies on discrete cubesBlock decompositions in the p-adic Langlands correspondenceSemisimplicity, purity and Mumford-Tate conjecture for hyper-K\"ahler varietiesSpecial Loci in the Moduli of CurvesOn the structure of cert...

幾何学的構造と特殊関数とガロア表現 - 2026/10/6の論文55本

1 hr 50 min

arXiv math.NTの新着論文55本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-06/ The Riemann-Siegel remainder as a fractional summandGaps, isolated points, and the origin of the ray in the one-dimensional Dirichlet spectrumExponential generating functions for Apostol-Dedekind and related sumsNonvanishing of special $L$-values of cusp forms on $\mathrm{GL}(2)$ with totally split prime power twists: without the class number hypothesisOn Mahler $U$-numbers under rational mapsOptimal large sieve for fixed order charactersMoments and Large Geometric Monodromy for Linearly Constrained Kloosterman FamiliesSequential exponential-motivic periods in spatially cut-off $\phi^4_2$Iterated cotangent-difference integrals over totally real cyclotomic fieldsPrescribed ideal classes and elliptic points in Ennola cubic fieldsCubic Progressions on Smooth Plane CurvesNote on fractional sum of the divisor functionFew small primes suffice to cover unit groupsBorwein-Bradley-type identities for Ramanujan-type series for $1/\pi^4$Supercongruences for Domb numbersProofs of some OEIS conjectures on Wythoff sums, Fibonacci and Lucas wordsThrough the lens of the Eisenstein idealError Term Estimates for Sets of RemaindersDyadic Structure of the Two-Block Odd Partition Function and Theta-Weighted Congruences for $pod(n)$An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebrasOn the generalized Sierpi\'nski and Riesel numbersOne-level density of zeros of the Riemann zeta function weighted by its special valuesThe main conjecture for a Vinogradov subsystemSharp mean value estimates in the absence of translation-dilation invarianceFour-square polynomial triples: quadratic classification and equal-degree obstructionsOn the factorization of $x^{d_{r}} + x^{d_{r-1}} + \cdots + x^{d_{2}} + x^{d_{1}} + p$ and a conjecture of C. NicolAb-faithfulness of absolute Galois groups in number theorySlope Stability for ${...

曲線と数論的構造と解析的ツール - 2026/10/5の論文28本

56 min

arXiv math.NTの新着論文28本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-05/ Arithmetic growth in partially commutative semigroups of endomorphismsThe proportion of polynomials over F_2 with positive orthogonal multiplicityShimura Reciprocity for Real Quadratic FieldsCounterexamples for Rational Points Near CurvesThe Prime Wavelet Tree: Compressing the Carmichael NumbersExtreme values of Dirichlet $L$-functions on the critical line with a growing prime modulusA uniform degree bound for modular rank-two Nahm sumsThe Wang--Sun Sum over Affine DerangementsA new upper bound for the irrationality exponent of $\zeta(2)$some arithmetical aspects of the two dimensional jacobian conjectureTelescopic Structure of Numerical Semigroups Generated by Unsigned Stirling Numbers of the First KindCohomology of Linearly Constrained Kloosterman Families: Newton Polytopes, Weights, and Boundary MonodromyCubic arithmetic-geometric mean and isogenies of Hesse elliptic curvesSplit-Cubic Curves from D(n)-Triples: A Bounded Finite-Field CensusPellarin's Identity, Carlitz Period, and Anderson Generating Functions over Arbitrary CurvesThe quality plane of $abc$-triples and the decomposition into gainsGosper's and Ramanujan's infinite products and generalizationsA cubic Chabauty criterion for hyperelliptic curvesEisenstein congruences in tame families and the class group of a metabelian extensionSum-product patterns in the shifted primesHausdorff dimension for exactly approximable matricesExplicit second moments of symplectic Siegel transformsQuantitative Gowers uniformity of the primes in intervals of length $X^{5/8+\varepsilon}$Exact diameter compression for four-point sumset cardinalitiesPappas's conjecture on ramified unitary local modelsResolving Erd\H{o}s-Ulam Monochromatic Union-Closed Family ConjecturesSharp rational points counting near nondegenerate curves in $\mathbb{R}^n$Sturmian beta-shifts do not have typical periodic optimization

方程式と素数と集合の構造 - 2026/10/2の論文35本

1 hr 11 min

arXiv math.NTの新着論文35本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-02/ Two-Line Elimination and the Weierstrass Group Law in Arbitrary CharacteristicPageRank on Lubotzky--Phillips--Sarnak graphsSome Methods to Solve the Diophantine Equation ay^2=b(x^k-c^k)An explicit family of twists of the Carlitz module with unbounded analytic rankNew bounds for the integer Chebyshev constant of [0,1]On a problem on Ramanujan-Sato series of level 11Perfect squares in reciprocal-sum sequences and primes that are inert in quadratic fieldsCongruence Jumping in Polynomial Divisibility Systems: Arithmetic Structure and Solution SetsMultiplicative recurrence of Piatetski--Shapiro and nil-Bohr setsTranscendence of dendric beta-expansions with pure discrete spectrumPowers in orbits and semigroups generated by polynomialsConstruction of parametrized families of general pseudo-bimagic and bimagic squaresBaire-category transfer between Engel and Pierce expansionsIndefinite theta vectors and generalized Nahm sums of arbitrary rankThe sixth moment of the Riemann zeta functionTranslation invariant quadratic forms in $8$ variables and dense sets of primesSharp $p$-adic Extrema and Least Extremal Rows for Restricted Binomial GCDsA Prime-Power Dichotomy for Nekrasov--Okounkov Hook Lengths and $t$-Core PartitionsTridimensional character sums with polynomial arguments and applicationsUniform estimate of Lang-Weil type for counting points of schemes over finite ringsQuadratic distances in even dimensions over prime fieldsAverages of Artin characters and their relation to the Davenport--Heilbronn theoremSquare products of factorials and a conjecture of Erd\H{o}s and GrahamSupersingularity and Superspeciality Verification of Abelian SurfacesInfinite free pro-p products as absolute Galois groupsOn the prime geodesic theoremOn The Index of Polynomial Compositions over Valued FieldsDirect Group Laws on Classical Genus-One ModelsMarkov chains arising in...

L関数とモジュラー形式とガロア群 - 2026/10/1の論文29本

59 min

arXiv math.NTの新着論文29本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-01/ A Romanoff-type theorem for a multiset of products of powersStrong Artin Conjecture for Generalized Octahedral Representations in $\mathrm{GL}_3$Large gaps between Romanoff numbersEuclidean Triangles Associated with Diophantine $D(4)$-triplesZeta elements for $p$-ordinary modular forms over imaginary quadratic fields and applicationsMonogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomialsOn a problem of Nathanson related to strongly minimal asymptotic bases of order $h$The twisted convolution identity and ghost $r$-SICs from finite quantum dilogarithmsThe cardinality of a set containing the pairwise sums of four positive integersLimit distribution of algebraic integral points on curvesFinite-slope p-adic L-functions for $\mathrm{GL}_{3}$On the Quotient of a Pseudo-null ModuleAsymptotic and Arithmetic Aspects of Generalized Colored OverpartitionsThe sixth moment of a degree two $L$-function of arbitrary levelAtkin--Lehner Quotients of Modular Curves at Primes of Bad ReductionSharp spherical extension theorem in $\mathbb F_q^{2m}$ and applicationsOn a question of Jones on tracelike vectors, cusp forms, and von Neumann algebrasRational quadrilaterals and tetrahedra -- the involutions of Kummer, Heegner and ReggeGalois groups of random polynomials of large degreeSemi-stable models, local heights and quadratic Chabauty for $X_0(N)^*$A proof of Hirose's duality conjectureResurgent rigidity of mock theta functions: uniqueness and natural boundary crossingOn Greenberg's conjecture for rational elliptic curves at Eisenstein primesOn c-polynomial factorisationsThe Bias Conjecture for One-Parameter, Non-Isotrivial Elliptic Curve FamiliesOn the coefficients of the asymptotic of analytic torsionCanonical representatives and interval independence in Ekedahl's equivalenceDiameter and radius of an additive-multiplicative graphOn...

予想と近似と数論的関数 - 2026/9/30の論文39本

1 hr 18 min

arXiv math.NTの新着論文39本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-30/ Proofs of some conjectures by Bringmann, Han, Heim, and Kane on periodic sign changes in eta-quotientsPrimes in arithmetic progressions and Siegel zeroesp-adic Rigidity and Supercongruences at Rank Two AttractorsStrongly Pseudoperfect NumbersA $q$-analogue of a binomial supercongruenceOn closed-form expressions for weighted mean square of the Riemann zeta function and Dirichlet $L-$functionsOn Vojta's harder implication, height inequalities for admissible pairs, points of bounded degree and Deligne-Mumford stacksTwisted Diophantine Approximation I: Asymptotic TheoryTwisted Diophantine Approximation II: Uniform TheoryReduction of Weil-Deligne RepresentationsFarey Symbols for the Picard GroupA Local Approach to Monogenity with an Application to Lenny Jones' ConjectureThe Index of Composition of polynomials and its applicationsCollective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier RefinementsOn Boston's Unramified Conjecture for $\GL_2$ and McLeman's $(3,3)$-ConjectureThe Algebra of Parity-Twisted Crank Moments and a Prime-Detecting ExpressionTruncated pretentious distances of multiplicative arithmetic functionsOn an infinite family of cubic fields with explicit fundamental unitsProducts of two elements of Granville's random model in residue classesMultiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type ConjectureA closed-form law for the Salikhov-Zeilberger-Zudilin-Bai family, and computational evidence that Bai's point is optimalWeighted equidistribution of factorial prime valuations in fixed power bandsAn infinite family of counterexamples to Goss's conjecture on L-functions of cyclotomic function fieldsA negative answer to Erd\H{o}s Problem #786Uniform Estimates for Integers with a Large Smooth PartA Short Proof of a Theorem of Pan and ZhangAx-Schanuel for the Drinfeld $j...

楕円曲線とゼータ関数と素数と分割関数 - 2026/9/29の論文67本

2 hr 21 min

arXiv math.NTの新着論文67本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-29/ Tamagawa numbers and torsion of elliptic curves over function fieldsEfficient Computation and Congruences for Colored Partition FunctionsQuasimodular Forms, Partitions, and Primes in IntervalsConductors and Quadratic base changeFactorizations in algebraic monogenic semidomainsUnit fractions with semiprime denominators: an elementary proof of Erd\H{o}s Problem #306On the sum of odd minimal excludants over overpartitionsMatrix Solutions to the Diophantine equation $X^4+ Y^4=2Z^4$On the Ordering and Injectivity of Lagrange Constants Associated with Certain SubstitutionsOn Fermat-type equations of signature $(r,r,p)$Congruences for Overcolored Partition $k$-tuples Restricted by Parity of the PartsLower Bounds for Moments of Automorphic L-functionsThe infinite sum of the cubes of reciprocal balancing numbersPseudo-Effectivity in the Skolem-Mahler-Lech TheoremSkew cyclic codes through Drinfeld modulesAdelic reduction of module latticesA Unified Approach to Formal Arakawa-Kaneko Type Zeta Values via Iterated IntegralsEscape and Non-Escape of Mass for Monogenic Binary Cubic FormsMore than 83.69% of the zeros of the Riemann zeta function are distinctDynamics of multiples of zeta by exponential functionsStacky Heights, Entropy, and Zeta Functions of Weighted Hypersurfaces over Finite FieldsThe Beilinson--Bloch heights of generalized Ceresa cyclesPrime-Detecting Identities from Dirichlet InversionOn the distribution of the zeros of the Euler double zeta-function $\zeta_2(s,s)$A Padovan-automatic description of a nested recurrenceAn elementary treatment of Ramanujan's elementary continued fractionsCancellation profiles of Fibonacci-Lucas zeta sums$k$-Fibonacci and $k$-Lucas numbers with the H\"older inequalityBiases in the distribution of primes in short intervalsCyclotomic factors and irreducibility of the denominators of $q$-deformed rational numbersNece...

合同式と楕円曲線とガロア群とゼータ値 - 2026/9/28の論文28本

56 min

arXiv math.NTの新着論文28本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-28/ A Congruence Conjecture of Z.-W. Sun for Reciprocal Central Binomial SumsSupercharacter theory and applications to Ramanujan sums over a finite Frobenius ringOn the Langlands--Kottwitz--Scholze methodCongruence obstructions in the refined Koblitz conjectureLocal Weak Maass Forms and Traces of Cycle IntegralsPinch's conjecture on $a$-convexityMishiba's Conjecture on the Coaction of $\infty$-adic Multiple Zeta ValuesCounterexamples to the inhomogeneous Duffin-Schaeffer conjecture for a residual set of shiftsUpper and lower fluctuations in Shallit's law of leap years in Pierce expansionsCounterexamples to the inhomogeneous Duffin-Schaeffer ConjectureOn the Moments of Least $r$-Gaps of Partitions and a Conjecture of Baruah and TalukdarThe derivative function of the zeta-star correspondenceExperiments on $3$-isogeny Selmer groups of elliptic curves with a $3$-torsion pointA parametric Catalan-type congruence for generalized central trinomial coefficientsIrreducible rootless unimodular lattices generated by vectors of norm $3$Ternary Perfect Forms Over Imaginary Quadratic FieldFurther Results on Sum-Freedom of Binary and $q$-ary FunctionsOn Conjectures of $\mu$-Invariant for Selmer Groups at $p=2$Computing the Iwasawa $\mu$-Invariants for Elliptic Curves over $\mathbb{Z}_2$-ExtensionsOn the infinite sum of reciprocals of the fourth powers of balancing numbersFree semigroups of power seriesGalois groups of integer polynomials with prescribed coefficientsFormal groups and $(\varphi,\Gamma)$-modulesGalois groups of twisted reciprocal polynomials: a uniform asymptoticThe geometry of solutions to the general sexticCartier--Dieudonn\'e Theory of Connected Group SchemesComment on "Symmetric Pseudo-Random Matrices"A Mathematical Theory of Near-Field Super-Resolution

モジュラー形式と有限体とゼータ関数 - 2026/9/25の論文39本

1 hr 23 min

arXiv math.NTの新着論文39本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-25/ Rank-two Nahm sums, modularity obstructions, and the McKay--Thompson series $T_{31A}$Noncongruence cusp forms, Veech groups and enumerationEffective logarithmic two-point Chowla bounds in every windowPermutation binomials of the form $X^r(X^{q-1}+a)$ over finite fieldsStraight-line programs for the solutions of Pell's equationComputations of Cohomology of Arithmetic Groups, Part 1On the index of generalized trinomials over Valued fieldsComputing the cohomology of Shimura curves in quasi-linear timeCongruence Classes of Supporting the Erd\"{o}s-Straus Conjecture II: Wild SolutionsA new lower bound for the Schur-Siegel-Smyth trace problemRefinements of Peck's theorem on simultaneous approximation to algebraic numbersCounting consecutive multiplicatively dependent triplesA geometric proof of Peck's theoremA power-sum obstruction to cyclotomicity in a family of symmetric numerical semigroupsLie algebras for multiple Eisenstein series and multiple q-zeta valuesThe Fermat-Type Matrix Equation over $\mathrm{GL}_2(\mathbb{Z})$Reducibility of $rx^m+p^e f(x)$ for Large Primes $p$On murmurationsArithmetic progressions in dense subsets of primitive elements of finite fieldsSelf-intersection Points of Billiard Trajectories in a Square with Small PocketsOn the density of $A+B$ when $B$ has few elementsOn smooth elements in arithmetic semigroupsInfinitely Many Off-Critical-Line Zeros of the Tempered Xi Function: A Disproof of Yang's ConjectureIdentities and congruences involving orthogonal polynomials and Ap\'ery-like numbersA note on isomorphism types of complete discretely valued fields of mixed characteristicComputing the divisor summatory function in $N^{9/28+o(1)}$Sparsity of rational points on torsion level covers of Hilbert modular varietiesDiophantine approximation by primes and Landau--Siegel zerosLonely Runner RelationsThe Schur multiplier of $\rm{S...

ゼータ関数とL関数と保型形式 - 2026/9/24の論文41本

1 hr 23 min

arXiv math.NTの新着論文41本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-24/ A new upper bound for the irrationality exponent of zeta(3)The Primitive Generalized Fermat Equation x^3+y^5=z^7: A computer-assisted proofGalois-Orbit Structure, Ramanujan Sums, and Stable-Range Collapse for Cyclotomic Cosine Formulas$A_2$-frames, negacyclic glue, and extremal strongly $6$-modular latticesThe number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular varietyDefinability and undecidability via the torsion subgroup of unitsCompleted cohomology of Hilbert modular varieties below middle degreeGeometric lifting and Freiman's $3k-4$ theorem in compact connected abelian groupsA proof of the Baruah--Gogoi conjecture on sums of odd and even overlined partsInfinite families of pairs of real quadratic fields whose class numbers are divisible by a given integerDefinite integral Albert algebras: arithmetic and finite geometryModular integrals for individual modular knotsConstruction of vector-valued adelic automorphic formsZero density estimates for $\mathrm{GL}_2$ automorphic $L$-functionsGevrey localization for simple and distinct zeros in a prime-modulus Dirichlet familyAn Approximate Version of Vu's Theorem on Economical Subbases For Non-Integer ExponentsShifted log-sine integrals and multiple zeta valuesMorse Topology, Zero Products, and Elliptic Prime CrossingsOn some $D(u^2)$-triples and quadruples of triangular numbersBeyond the unique pair: a two-parameter family of rational triangles with equal perimeter and areaThe Arithmetic of Reducible Rank 2 Hypergeometric MotivesAn Introduction to the Lagrange and Markov Spectra through the Lens of Generalized Markov NumbersWeighted bilinear identities and supercongruences for Ap\'ery-like polynomialsOn the hyperbolic prime number theoremDistinguishing Gauss sumsA tyro's approach to the tilted sieve: beyond the Erd\H{o}s--Rankin boundCounting $k$-tuples of posi...

素数とp進数と格子と多項式とゼータ関数 - 2026/9/23の論文45本

1 hr 33 min

arXiv math.NTの新着論文45本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-23/ Infinitely Many Binomial Coefficients of Deficiency OneCarmichael numbers of the form $2^n p^m+1$ with odd exponent $m$: refinements of a theorem of Florian Luca, a general independence lemma, and a computational studyAn Integral Representation of the Generalized Fibonacci NumbersBrauer-Kuroda relations for ramified graph coversThe Sphere Packing Problem in Dimension 4 and the Twenty-Four-Cell ConjectureMoulds, Bimoulds, and some Lie algebrasA density version for the sum of nine cubes of primesOn the Euler transform and the floor functionDistinct exponents in the prime factorizationIrreducible polynomials with restricted digits in base $b(T)$On the generation of multiplicative groups by small primesThe density of sums of distinct divisorsDensity of large holes among power-free lattice pointsA surprising generalization of the M\"{o}bius functionS-integrality for families of ordinary K3 surfaces and algebraicity theoremsOn the positivity of truncated pentagonal number series and some conjectures of MercaIrrationality Exponents and Partial Quotient Growth in Continued FractionsAbelian $p$-extensions with restricted $p$-ramification and the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q} (\sqrt{q})$The large sieve through Parseval, Large sifted sets are regularThe weighted large sieve through ParsevalLarge values of the Hurwitz zeta function with rational parameterEqual subset sums and close divisorsBoyd's conductor-11 Mahler measure conjecture: proof of the split-integral identity (C3), with an exact structural analysis of the family S_kA certified continuation machine for Mahler measure identities at CM points, with twelve new proofs of conjectures of SamartPeels of Equilateral Triangulated SurfacesOn two families of period integrals related to Catalan's constantImproved rational approximations to Catalan's constantCokernels of random $p$-adic...

ゼータ関数と素数とガロア群と楕円曲線 - 2026/9/22の論文62本

1 hr 44 min

arXiv math.NTの新着論文62本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-22/ Superpolynomially Large Support in Every Irreducible Factor of Lacunary PolynomialsIwasawa theory of class field towersA quadratic-residue dichotomy for two partition functions modulo 3On periods of the Tribonacci sequence modulo primesMonogenic Fields of Cryptographic SizeBad Reduction of Genus Two Curves with complex multiplicationAlmost Trivial Units in Group RingsZero density theorems for short intervalsMaximal Unramified $p$-Extensions with Prescribed Galois Groups: A Quantitative Refinement of Ozaki's TheoremOn a Tur\'an's theorem for small primesOn a Tur\'an's theorem for arithmetic progressionsRomanoff type theorems for polynomials over finite fieldsSteinness of the Basic $\mathrm{GL}_n$ Local Shimura Tower in Odd RankOn $\mathbb{Z}_2$-extensions of real quadratic fields with class group of $2$-rank threeCounting number fields with symplectic Galois groupThe variance of the number of lattice points in narrow sectorsExplicit bounds for the prime number theoremWave Numbers: Discrete Sequence Algebras, Sieve Projectors, and Dynamical Geometry$v$-adic Chowla-Selberg formula over function fieldsCritical Pairs for Mixed Restricted Sumsets in Prime FieldsA two-step supercongruence for an Ap\'ery-like sequenceLarge values of quadratic Hecke $L$-functions with prime-related moduli of the Gaussian fieldLower-order terms in mean-square formulas for the Euler--Zagier double zeta-function and regularized multiple zeta valuesHigher Reciprocity, Cassels Pairings, and Selmer Towers for the 3/5 Congruent Number ProblemRefined sum formulas for finite multiple zeta values of level twoTwo Legendre-symbol determinants of Sun and Bernoulli numbersConcave transforms and volumes of adelic line bundlesSelmer groups of CM-twists of elliptic curvesInterpolation determinants and the Lebesgue--Nagell equation $a^2-D=b^p$On the noninjectivity of Jordan's totient fun...

格子とディオファントス近似とガロア環 - 2026/9/21の論文19本

33 min

arXiv math.NTの新着論文19本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-21/ On permutation-invariant construction of glued latticesExtreme value laws for intrinsic Diophantine approximation on spheresEigenvectors of $p$-Curvature for Geometric Difference EquationsGalois deformation rings and modularity in the residually reducible caseOn The Cyclicity of Algebraic LatticesThe large sieve for square moduli under Hooley's hypothesis $R^*$Annular Frobenius Classification of p-adic Stieltjes--Schwarzian EquationsThe integer group determinants for $\mathbb{Z}_p^n$Difference of the Sum of All Odd and Even Overlined Parts of OverpartitionsFrobenius Numbers Associated with Primitive Pythagorean QuadruplesArithmetic structure of $L_2$-norms of ${\mathrm{SL}}_2(\mathbb{Z})$ matricesA Note On Certain Minimal Excludants Over OverpartitionsOn low-discrepancy sequences and Poissonian pair correlationHigher Labute-Serre duality and Lyndon wordsNon-existence of sets with few special directionsReal quadratic fields and finite quantum dilogarithms I$\mathbf{Bad}(\mathbf{r};\mathbf{s})$ is Hyperplane Absolute WinningAn equivariant version of Gabber's lemmaOn the Injectivity of Elementary Symmetric Partitions and the Multiset Recovery Problem

素数とガロア群と有限体と和集合 - 2026/9/18の論文26本

44 min

arXiv math.NTの新着論文26本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-18/ Asymptotic counting of integers with prime factors $p_{r^a s^b}$Endoscopic description of the local Langlands correspondence for $\mathrm{G}_2$A uniform proof approach for congruences modulo 3 for partitions with $k$-colored odd partsA new family of maximal curves not covered by the Hermitian curveSimultaneous nonvanishing of quadratic twists via Rankin-Cohen bracketsFinite subgroups of outer automorphism groups of the absolute Galois groups of mixed-characteristic local fieldsNorms of Schneider--Teitelbaum Polynomials in $p$-adic Fourier TheorySampling and Moments of Reciprocal Quadratic Mellin IntegralsOn a question of Ruzsa about densities of sumsetsA characterization of Sophie Germain primes - IIThe Three Gates: A Rooted-Operator Approach to Weil PositivityA problem of Yang and Chen on weighted representation functionsLow moments of automorphic random multiplicative function sumsFinding New Limit Points of Mahler Measure by Methods of Missing Data RestorationComputational results on sums of a prime with squares or cubesRogers--Ramanujan identities from the geometry of $X^a=Y^b$An ergodic approach to equations of the form $x+y=\lfloor\alpha(n)\rfloor$Sumsets of Ahlfors--David regular setsOn the Hiraga-Ichino-Ikeda conjecture on formal degrees for $\mathrm{G_2}$A complete classification of permutation binomials of the form $X^r(X^{q-1}+a)$ over finite fieldsInfinite prime sumsets in structured and $U^k(\Phi)$-uniform setsConductor-Discriminant Inequality for Tamely Ramified Cyclic Covers IConductor-Discriminant Inequality for Tamely Ramified Cyclic Covers IILogarithmic--exponential preparation in sharply o-minimal structuresCombinatorics of hyperplane arrangements and Witten zeta function at the originMorphism spaces on low degree hypersurfaces

L関数とゼータ関数とモジュラー形式 - 2026/9/17の論文36本

1 hr 1 min

arXiv math.NTの新着論文36本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-17/ Distinct Consecutive ProductsTranscendence measure for the values of the logarithmic derivative of the Bessel function $J_0$ at algebraic argumentsLattice points close to a smooth curve and squarefull numbers in short intervals. IIEffective Hecke eigenvalue equidistribution over the Atkin--Lehner subspacesOnly finitely many modular Jacobians are supersingular modulo a given primeOn two forms in many variables of different degreesZero-Density Concentration for Dirichlet PolynomialsUnramified Geometric Iwasawa theory of function fieldsSurjectivity of the Enots Wolley SequenceContinuous approximation to the reciprocal sum of the cubes of Fibonacci numbersExact universal normalizations for the G\'al--Koksma lemmaNonvanishing of ray class $L$-functionsA $q$-recurrence for a finite Ap\'ery limitGraded Algebras of Modular Forms and Sign Changes of Fourier Coefficients for Eta QuotientsBounded intervals containing a given number of primesExtreme Values of Quadratic Dirichlet $L$-Functions over Monic Irreducible Polynomials in $\mathbb{F}_q[t]$Cyclotomic Prime ExtractorsPeriodicity conjectures for all 2-sumfree sequencesExtreme values of Euler-Kronecker constants of cubic abelian fieldsStable Trace Formula for Newton strata of Shimura varietiesOn Multiple Eisenstein Series in Positive Characteristic: Direct Sum ResultOn a conjecture of Browning and Sawin on random hypersurfaces with sign coefficientsA uniform effective Andr\'e--Oort resultAn Omega result for partial sums of the Riemann zeta function$\Omega$-results for the logarithmic derivative of $\zeta(s)$ on vertical homogeneous progressionsArithmetic Constraints and Limit Laws for Diagonal Rational PartitionsFinite Fourier Duality, Radial Values, and Arithmetic of a Mod Eight False Theta QuotientTranscendence criteria for the minimal word of the rational base $3/2$Tunnell-type criteria for variants...

L関数と楕円曲線と数体と素数 - 2026/9/16の論文38本

1 hr 4 min

arXiv math.NTの新着論文38本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-16/ The Waring-Goldbach problem in short intervals under the Generalized Riemann HypothesisMean Lindel\"of Hypothesis and Prime Geodesic Theorem on Bianchi ManifoldsA formula for the rank over $\mathbb{Q}(t)$ of the elliptic curve $y^2=x^3+At^6+Bt^3+C$Number fields as curves over $\mathbf{F}_1$Simultaneously small continued fraction entropy and base $b$ entropyElementary proofs of congruences modulo 5 for overpartitions with restricted odd differencesRational Points near Monofractal Curves and the Strong Oscillation PrincipleLocal Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrizationLocal Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrizationTwisted Rational Zeros and Local-Global Principles for Linear Recurrence SequencesHigher Schwarzians of Elliptic Double Covers and Eisenstein--Kronecker FunctionsThe Furstenberg-S\'ark\"ozy theorem for sums of an even number of odd powersAn infinite family of imaginary biquadratic fields with a large class numberLaurent series expansions for the Barnes multiple zeta functionTriple divisor type functions in arithmetic progressions to prime power moduliIwasawa theory of (directe) Cayley graphsThe Local Ghost Theorem in the Tr\`es Ramifi\'e CaseDistribution of squarefree integers with double congruence conditionsPrime-power congruences for level-one eigenformsExtreme values of quadratic Hecke $L$-functionsOn $t$-sumfree sequencesMixed moment of $GL(2)$ and $GL(3)$ $L$-functions in the level aspectAn additive problem in connection with some quadratic real fields with class number onePowers of the Thue--Morse Series: 2-Adic Valuations and Automatic Odd PartsRefined conjectures on Fitting ideals of BDP Selmer groupsModular functoriality for finite groupsUniform Mordell-Lang conjecture for semiabelian varietiesA class formula for effective Anderson motivesOn Sarna...

素数と楕円曲線とモジュラー形式 - 2026/9/15の論文69本

1 hr 57 min

arXiv math.NTの新着論文69本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-15/ The Strong 24-ConjectureTheta functions after WeilDynamical uniform boundedness for unicritical polynomials and elliptic curves of large rankArithmetic Siegel-Weil for the spherical Hecke algebraGalois representations and modularity for twisted moments of Kloosterman sumsPointwise ergodic theorems along sequences of intermediate growthSpherical statistics and phase transitions in high-dimensional latticesFiniteness of an Isogeny Class via EquidistributionPrime and Nonprime Totatives: A Sharp Construction and Exact ThresholdsThe optimal scale in Linnik's microsquare problem for almost all integersGeneralized Wieferich primes and monogenic polynomialsDensity of Vanishing of Certain Eigenspaces of Cyclotomic Class GroupsA Local Proof of Langlands's Second Main Lemma for Local Epsilon Factors over Nonarchimedean Local FieldsModular and Shimura curves $X_0^D(N)$ embedded in $\mathbb P^1 \times \mathbb P^1$Reduction of integer tiles via CRT and base-p digitsPatterns in the Markov numbers and their generalizationsQuantitative linear independence for square rootsTwisted Lubin-Tate Big Witt Vectors and Fleck-Sun-Wan CongruencesOn Decomposition of Drinfeld cusp forms of level $t$Golden-ratio growth of Conway's subprime closureTwo-Height Approximation and Mahler's Problem on Liouville NumbersA Central Limit Theorem for Coprime Pair Counts in Randomly Translated DisksSurjectivity of Finite Rank-Capped Enots-Wolley SequencesThe Jensen--P\'{o}lya program and inequalities for arithmetic sequencesCubic AGM graphs and Hessian $3$-isogenies over finite fields $\mathbb{F}_q$ of odd characteristic with $q \equiv 2 \pmod3$Character sums on an oriented singer conic and explicit Ramanujan double coversAn explicit power-saving bound for S\'{a}rk\"{o}zy's Theorem on shifted primes, assuming GRHBloch cycles and the weak two-variable Chinburg conjectureDynamical generali...

L関数と楕円曲線とモジュラー形式 - 2026/9/14の論文25本

42 min

arXiv math.NTの新着論文25本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-14/ An adelic approach to the Kudla-Millson lifts over totally real number fieldsLocal-global principles for visibility of lattice points on parameterized curvesOn the variation of slopes over moduli stacks of Galois representationsCritical convergence and Hausdorff measures for generalized Flint Hills series$S_h$-sets in abelian groupsA Generalization of S\'ark\"ozy's theorem in function fieldsZeros of Quasimodular Forms Defined by Iterated SumsThe first moment of quadratic Dirichlet $L$-functions in the even hyperelliptic ensembleTight universality of $m$-gonal forms with minimal criterion setsGauss Genus Theory in Characteristic 2Projective Kernels and Replicability in Modular Function TheoryClassification of torsion of elliptic curves over quintic fieldsLarge fluctuations of extended Rademacher random multiplicative functionsProjection and fibering in groups of bounded exponentKronecker sequences beyond the torus: nearest-neighbour distances and best returnsIwasawa theory of CM elliptic curves at potentially supersingular primesKolyvagin's conjecture at non-ordinary primesAn asymptotic formula for a cubic moment of $GL_2$ $L$-functionsJacquet--Rallis transfer for GL(2)Quasipolynomial density bounds for $K$-point configurations in $\mathbb{Z}^d$Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued FractionSerre's problem on statistics of Brauer symbolsPoincar\'e duality for pro-\'etale $\mathbf{Q}_p$-local systemsCharacteristic Classes of Adelic Vector Bundles and ApplicationsNon-archimedean Monge-Amp\`ere measures for toric metrics on subvarieties of toric varieties

L関数と多項式とゼータ値と行列 - 2026/9/11の論文26本

44 min

arXiv math.NTの新着論文26本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-11/ A New Sparse Algorithm for Polynomial GCD over IntegersSums of distinct divisors of factorialsOrdinary 3-Isogeny Graphs and Improvement of Supersingularity Testing for Twisted Hessian Curves over Prime FieldsEffective estimates for exponential sums with multiplicative coefficientsRational Approximations for Reciprocals of Multiple Zeta Values and Trivariate Cauchy NumbersA $p$-adic monodromy theorem for curvesMoments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short IntervalsLog-crystalline representations and $(\varphi, \Gamma)$-modulesThe irrationality measure of {\pi} is at most 7.101862832357On the bounded-conductor finiteness conjecture in equal characteristicSharp unconditional moment bounds for products of L-functionsInternal congruences modulo powers of $2$ for overpartition tuples with odd partsGeneralized Frobenius Partitions Modulo Powers of $2$Bounded asymptotic bases for linear formsChowla's non-vanishing conjecture over $\mathbb{F}_q(T)$The asymptotic in Waring's problem over function fields beyond twice the degreeOn the Mahler measure and root distribution of the $Q$-polynomial of linksThe 2-Adic Valuation of the Order of the All-Ones Class in the Sandpile Group of a SquareF-theory on K3 surfaces and orthogonal modular formsA dynamic point of view on universality for random matrices over finite local ringsQuantitative universality for products of i.i.d. random matricesRankin--Selberg integrals of opposite conductor--one newformsDivisibility and torsion in higher Chow groups over arithmetic fieldsReversibility and its asymptotic counting in Picard groupA maximal function field of genus $17$ over $\mathbb{F}_{11^2}$Cusp restrictions and Bunke--Naumann invariants with level structure

楕円曲線とL関数とディオファントス近似 - 2026/9/10の論文33本

55 min

arXiv math.NTの新着論文33本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-10/ A proof of Hare's $\epsilon$ unfair conjectureThe density of long runs of non-$r$-free integersSpectral Algebras of Abelian Cayley GraphsTriple intersections for algebraic curves on the real torusCyclotomy of symmetric polynomialsEffective Euler SumsThe addition on totally positive integers uniquely determines the totally real number fieldGeneric Manin-MumfordRegular Arithmetic Functions, Volume I. Theory, Applications, ExamplesWhat Does MMLU Actually Measure? A Psychometric Audit of Difficulty Structure in Aggregate Benchmark ScoresModels of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-IsogenyInteger group determinants for the elementary abelian group of order 49The three Kanade-Russell identities modulo nineFrom Pythagorean Runs to Pell-Generated Cubic RunsAn elementary approach to Sun Kim's general theta function identitiesUniversal norms and de Rham representationsUnramified Motivic Alternating Multiple Mixed ValuesNon-vanishing of symmetric square $L$-functions in the weight aspectPencils of norm form equations and a conjecture of Thomas, IIDiophantine approximation with primes in an arithmetic progressionA Counterexample to a Conjecture of Liu and Qian and a Refined Inverse Theorem for Restricted Sumsets in $\mathbb{Z}_p$Inertial multiplicity bounds for two dimensional projective representations and bounds for the number of $\operatorname{PSL}_2(\mathbb{F}_q)$ and $\operatorname{PGL}_2(\mathbb{F}_q)$ number fieldsFaltings' Isogeny Theorem via EquidistributionQuasi-modularity of symmetric quasi-shufflesSharp local estimates for smooth numbersOn the syntomic regulator of the Hesse cubic curves and $p$-adic hypergeometric functionsInteger group determinants for abelian groups of order 24On the Number of Hecke Eigenvalues of Same Sign on $\mathrm{GL}_n$Irreducibility of truncations of the Catalan generating function$B_h$-...

円分体とp進解析と楕円曲線とL関数 - 2026/9/9の論文81本

2 hr 17 min

arXiv math.NTの新着論文81本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-09/ Lower bounds for some value sets over finite fields: incidence geometry and Bourgain's group expansion theoremOn the Diophantine Equations Arising from Three-Term $b$-Concatenations in Pell-Type SequencesPrimes with Restricted-Digit DifferencesOn the classification of small cyclotomic integersOn the class number of certain cyclotomic fieldsA $q$-microscope for mock-theta denominator patternsInfinite-order $p$-adic differential equations for Hurwitz-type Euler zeta functions: Higher-dimensional extensions and uniqueness of bounded solutionsThe entropy of coclass one and of SmallGroup(729,45)Central non-vanishing of Dirichlet $L$-functionsFrom dimension four to dimension five in the Tate conjecture for abelian varieties over finite fieldsLattice point visibility along polynomials has density oneNormal Behavior and Periodic Points of a Pseudo-Aliquot Map Associated with the Dedekind Psi FunctionMean Values and Normal Order of a Successive-Iterate Ratio of Dedekind's Arithmetic FunctionBounds on Whittaker Functions for $\mathrm{GL}(n)$Fields of definition of $p$-torsion points of elliptic curves and their ramificationMethods to Find Integer Points on the Elliptic Curve of Factorizable Polynomial EquationOptimization of Quadratic Sieve Algorithm Implementation for Large Integer FactorizationUnsupported Cyclotomic Divisors in Three-Prime Integer TilingsGeneralized Zeckendorf expansions of the 2nd orderA Fricke transformation for cubic-residue eta products of level 13High dimensional Riemann--Roch spaces in linear spaces with small squaresThree Irrationality Results for the Dilogarithm: Rhin--Viola and Viola--Zudilin Constructions at $-1/4$, $1/5$, and $-1/3$Maximising the number of solutions to linear equations$p$-adic properties of division polynomials and algebraic sigma functionsUpper bounds for arithmetic functions over polynomial values via Cheb...

ゼータ値と多項式と分布と格子点 - 2026/9/7の論文23本

41 min

arXiv math.NTの新着論文23本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-07/ Multiple zeta values in $\lambda$-ringsSIC dimension towers via cyclotomic polynomialsA counterexample to the Chung-Graham-Spiro gap-set conjectureHilbert's Irreducibility for $\mathbb{G}_m$Degeneration of monodromy in the theory of Eisenstein congruences for classical groupsNumerical experiments on the Hardy conjecture for the Gauss circle problemOn multiply induced charactersOn the Divisibility Relation $\sigma(n)\mid\sigma(n+h)$ and a Generalized Erd\H{o}s--Sierpi\'nski ConjectureDistribution properties of generalized polynomialsThe Right Edge of the Zero Set of the Fibonacci Zeta FunctionLattice point visibility along powers of quadratic polynomialsThe Prouhet--Tarry--Escott problem for subsets with small doubling in integral domainsCounting level-raising congruences using modular representation theoryLocal Jacquet-Shalika integrals and modifying factorsProof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius PartitionsF-sets of arbitrary finite widthDistribution of points near the origin in the $d$-dimensional Lagrange spectrumShort arithmetic terms express the cardinality of elliptic curves in Weierstra{\ss} normal form over finite fieldsCone upgrade for effective equidistribution and weighted Khintchine--Schmidt theorem on fractalsColeman Isomorphisms in Syntomic Cohomology and $\mathrm{THH}$A Log-Free $n^{1/5}$ Bound for Chowla's Cosine ProblemArithmetic PolyhedraCounting sets with given doubling via dimension

楕円曲線とガロア表現と素数と分割数 - 2026/9/4の論文29本

49 min

arXiv math.NTの新着論文29本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-04/ An upper bound for an exceptional automorphism groupPerfect numbers, Wieferich primes and the solutions of $\binom{2n}{n}\equiv 2^n \bmod n$Poissonian pair correlations for the three-particle Sutherland modelSkolem-Mahler-Lech in rings of positive characteristic: a shorter proof and a multi-dimensional generalizationFactorization patterns and fields of definition of $\ell$-torsion points on the Jacobians of genus 3 hyperelliptic curvesOn lifting representations and actions on curves of the metacyclic groups $C_{p^s}\rtimes C_m$Representation Defects and Cassels Pairings for Congruent Number CurvesResolving a conjecture on permutation polynomials over $\mathbb{F}_{2^n}$Odd denominators in the Lonely Runner spectrum for six speedsPrime-power Diophantine tuplesThe Klein-V\'elu septic, 2-Division, and modular function fields of level 14The derived set of multiple star polylogarithmsThe $\mathfrak{sl}_2$-algebra structure of multiple Eisenstein seriesSupersingular Elliptic Curves Without Inseparable Small Degree EndomorphismsOvercolored Partition $k$-tuples Restricted by Parity of the PartsArithmetic probability measuresThe groups $\operatorname{SL}_2(\mathbb{F}_{13})$ and $\operatorname{SL}_2(\mathbb{F}_{19})$ are Galois over $\mathbb{Q}$Galois representations ramified at one prime via relative deformation theoryOn the exponential sum over squarefree integersShort character sums of inhomogeneous polynomialsThe subconvexity problem for symmetric square $L$-functions in level aspectCatalan's constant is irrationalSome generalizations of Oort's conjectureConnections between colored restricted $b$-ary and ordinary partitionsExtension Problems for the Vladimirov--Taibleson Operator and the Hierarchical LaplacianFrom Ordered Bernoulli Levels to Critical-Line Geometry: Integer Quantization, Bernoulli Residual Phase, and Prime-Power SpectraA Fej\'er--Riesz...

ゼータ関数と楕円曲線と数論的近似 - 2026/9/3の論文27本

46 min

arXiv math.NTの新着論文27本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-03/ A lower bound for the Call-Silverman height in cyclotomic extensionsOn the cuspidal cohomology of Iwahori congruence subgroups of $\mathrm{SL}(3, \mathbb{Z})$Ranks and integer points on elliptic curves induced by Fibonacci triplesOn everywhere locally soluble varieties in families over toric basesWhen Fibonacci and Lucas Meet Smith: A Computational ExplorationJacquet-Zagier treatment of the beyond endoscopy trace formula for $\mathrm{GL}_2$Summing the reciprocal of the polynomial appearing in Fermat's Last TheoremBounding Selmer Groups of Superelliptic Jacobians via Class GroupsAffine Copies of Three-Point Patterns in Sets of IntegersOn the counting function of square-full numbersRegularised double shuffle relations for planar Arborified Zeta ValuesOn the Growth of Denominators of Simultaneous Best Diophantine Approximations in the Euclidean NormLarge values of cubic and quartic Dirichlet $L$-functions of prime moduliA Two-Variable Zeta Function for a Parity-Perturbed Hofstadter Q-Recursion: The Exceptional t = -1 Slice and Gaussian Boundary LayersThe Hasse norm principle for $A_4$-quartic extensions of global function fieldsImproved Weyl bounds on short intervalsOn the occurrence of congruence multiplicities between Ramanujan's theta functionsOn divergence related to Riemann--von Mangoldt's explicit formula of the prime-counting functionAdelic points and unmramified Brauer approximation for classifying stacksPetersson-Rigid Lattices in a Census of 100 Rank-Three Root BasesA new proof that more than $2/3$ of the zeros of the Riemann zeta function are simple and on the critical lineIterated-sumset spectra: The complete exponent law and its rank geometrySparse $k$-AP Covering Sets and the Arithmetic Kakeya Conjecture$\mathfrak{sl}_2$-action on the uri Lie algebraA finiteness theorem for geodesic Leech wheelsFourteen lonely runnersFinite extension...

ゼータ関数と指数和と代数体 - 2026/9/2の論文32本

55 min

arXiv math.NTの新着論文32本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-02/ Reducing Every Set of 36 Consecutive Integers to Zero by Differences of SquaresColombo's Determinant ProblemThe shortest harmonic sums with decreasing denominatorFrom Common-Slot Chains to Heisenberg Central Products over Global FieldsSmooth Diffeomorphisms and Mahler's Problem on Liouville NumbersAlmost $k$-th powers in short intervalsExceptional points on Atkin--Lehner quotientsExplicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta FunctionDistribution of Kaneko's val functionA unification of Euler-Maclaurin and Euler-Boole summation formulasImproved bounds in Birch's theorem for forms in many variablesUniversal murmuration and Hecke augmentationCovering Projective Height Balls by Subspaces in Rigid Adelic SpacesSharp lower bounds for shifted moments of Dedekind zeta functionsNonabelian Chabauty for the Thrice-punctured Line over Cyclotomic FieldsAn improvement on the largest prime factor of $n^2+1$New classes of trace-form permutation polynomials and their compositional inversesRegularized spectral expansion of a Rankin--Selberg period and momentsConfluence relations for $q$-analogues of multiple zeta valuesA General Construction of Codes from Drinfeld ModulesOn the Ramification of Quadratic Fields where there is a torsion growthA Proof of Fraenkel's ConjectureTen unknowns for Hilbert's tenth problem over the integersThe First Two Exceptional Boundaries for Sets with Few Subset SumsShifted poles and chamber cancellation for classical Witten zeta functionsInfinite transitivity of tame groups of automorphisms of affine spacesHodge--Tate splitting and Akizuki--Nakano vanishing in positive characteristicDeciding superellipticity and computing the Weierstrass normal formTwo-photon quantum Rabi models - Spectral degeneracy and symmetriesOn Algebraic Integrability of Vector Fields with Rational Function Coefficients th...

楕円曲線とL関数とモジュラー形式 - 2026/9/1の論文48本

1 hr 23 min

arXiv math.NTの新着論文48本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-01/ On weighted forms in many variablesStable Solutions to Generalizations of Fibonacci Relations of Higher Order$q$-Analogues of some supercongruences related to generalized Van Hamme-type supercongruencesCounterexamples to O'Neil's Period-Index Problem on Elliptic CurvesVanishing of $\mathrm{Sha}(A/K)[\mathfrak{P}^\infty]$ and its consequences for the anticyclotomic Iwasawa theory of $\mathrm{GL}_2$-abelian varietiesThe average number of rational preperiodic points of polynomials over $\mathbb{Q}$Analogue of Cardy's formula on the 60-degree parallelogram: a modular approachThe Shimura Lift and Hilbert Modular FormsKato's main conjecture for nonordinary modular formsLagrange spectrum for Diophantine approximations of complex numbers with real part equal to one halfLuo's Spectral Large Sieve Inequality on Short IntervalsBloch-regulator Principal Parts of Cyclotomic Iwasawa PseudomeasuresOn the special values of Berndt's generalized $L$-functionCounting integral points near a curve in the n-dimensional Euclidean spaceWallis-type products with polynomial exponents and the Dirichlet beta function at negative integersExact logarithmic Hausdorff and capacity exponents of the non-Brjuno setDifference of the modular function $\omega_{2}(\tau)$, revisitedEuler Characteristics of $\mathrm{SL}_4(\mathbb{Z})$ and $\mathrm{GL}_4(\mathbb{Z})$, and their cohomological consequencesOn supersingular isogeny graphs of Drinfeld modulesThe arithmetic of critical values II: critical elliptic curvesHecke Subalgebras and Local Newforms for the Metaplectic Double Cover of $\SL_2(\mathbb Q_p)$Average twin prime conjecture for elliptic curves in arithmetic progressions$D(N)$-quadruples in upper-triangular $2\times2$ integer matricesLower Bounds for Moments of $L$-functionsMatrix representations and arithmetic properties of jacobsthal numbers via binary 3x3 matricesSets whos...

二項係数とディオファントス方程式と格子点 - 2026/8/31の論文20本

36 min

arXiv math.NTの新着論文20本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-31/ The Sufficient Set of Congruences of Binomial Coefficients for PrimalityFinite and Symmetric Multiple $T$-ValuesDiophantine m-tuples of Triangular NumbersTrilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutionsAn Erd\H{o}s-Wintner theorem for second-order linear recurrent basesThe Multiplicative Persistence Conjecture: Resolving the \(2\)-Adic Obstruction for Nonzero Even TargetsDrinfeld modular forms of higher rank from a lattice-oriented point of viewGeneralized Fermat equation over number fieldsLattice points in high-dimensional $\ell^q$ balls with small radiiRational and integral values of rational functions at rational pointsNorm Principles for ${\rm Go}(q)$ and ${\rm Spin}(q)$The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete HypertoriRational torsion on simple genus two JacobiansHarmonic higher weight distributions, Simonis' approach of MacWilliams identity and momentsZero-free columns in character tables of symmetric groupsOn Frobenius rigidity for motivic cohomologyOn the number of $2$-dice games with prime power dice-sizeArithmetic purity of strong approximation for toric varieties with constant global sectionsBetti bounds for spaces of curves on varieties and Manin's conjecture for quartic del Pezzo surfacesOn Manin's conjecture for quartic del Pezzo fibrations

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