プレプリどんどん: math.NT

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 group Perfect numbers, Wieferich primes and the solutions of $\binom{2n}{n}\equiv 2^n \bmod n$ Poissonian pair correlations for the three-particle Sutherland model Skolem-Mahler-Lech in rings of positive characteristic: a shorter proof and a multi-dimensional generalization Factorization patterns and fields of definition of $\ell$-torsion points on the Jacobians of genus 3 hyperelliptic curves On lifting representations and actions on curves of the metacyclic groups $C_{p^s}\rtimes C_m$ Representation Defects and Cassels Pairings for Congruent Number Curves Resolving a conjecture on permutation polynomials over $\mathbb{F}_{2^n}$ Odd denominators in the Lonely Runner spectrum for six speeds Prime-power Diophantine tuples The Klein-V\'elu septic, 2-Division, and modular function fields of level 14 The derived set of multiple star polylogarithms The $\mathfrak{sl}_2$-algebra structure of multiple Eisenstein series Supersingular Elliptic Curves Without Inseparable Small Degree Endomorphisms Overcolored Partition $k$-tuples Restricted by Parity of the Parts Arithmetic probability measures The 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 theory On the exponential sum over squarefree integers Short character sums of inhomogeneous polynomials The subconvexity problem for symmetric square $L$-functions in level aspect Catalan's constant is irrational Some generalizations of Oort's conjecture Connections between colored restricted $b$-ary and ordinary partitions Extension Problems for the Vladimirov--Taibleson Operator and the Hierarchical Laplacian From Ordered Bernoulli Levels to Critical-Line Geometry: Integer Quantization, Bernoulli Residual Phase, and Prime-Power Spectra A Fej\'er--Riesz inequality for Dirichlet series The Prime Clockwork: A Dynamic Representation of Modular and Multiplicative Arithmetic Oort's conjecture for split unitary Shimura varieties

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 extensions On the cuspidal cohomology of Iwahori congruence subgroups of $\mathrm{SL}(3, \mathbb{Z})$ Ranks and integer points on elliptic curves induced by Fibonacci triples On everywhere locally soluble varieties in families over toric bases When Fibonacci and Lucas Meet Smith: A Computational Exploration Jacquet-Zagier treatment of the beyond endoscopy trace formula for $\mathrm{GL}_2$ Summing the reciprocal of the polynomial appearing in Fermat's Last Theorem Bounding Selmer Groups of Superelliptic Jacobians via Class Groups Affine Copies of Three-Point Patterns in Sets of Integers On the counting function of square-full numbers Regularised double shuffle relations for planar Arborified Zeta Values On the Growth of Denominators of Simultaneous Best Diophantine Approximations in the Euclidean Norm Large values of cubic and quartic Dirichlet $L$-functions of prime moduli A Two-Variable Zeta Function for a Parity-Perturbed Hofstadter Q-Recursion: The Exceptional t = -1 Slice and Gaussian Boundary Layers The Hasse norm principle for $A_4$-quartic extensions of global function fields Improved Weyl bounds on short intervals On the occurrence of congruence multiplicities between Ramanujan's theta functions On divergence related to Riemann--von Mangoldt's explicit formula of the prime-counting function Adelic points and unmramified Brauer approximation for classifying stacks Petersson-Rigid Lattices in a Census of 100 Rank-Three Root Bases A new proof that more than $2/3$ of the zeros of the Riemann zeta function are simple and on the critical line Iterated-sumset spectra: The complete exponent law and its rank geometry Sparse $k$-AP Covering Sets and the Arithmetic Kakeya Conjecture $\mathfrak{sl}_2$-action on the uri Lie algebra A finiteness theorem for geodesic Leech wheels Fourteen lonely runners Finite extensions of abelian schemes and duality for commutative group stacks

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 Squares Colombo's Determinant Problem The shortest harmonic sums with decreasing denominator From Common-Slot Chains to Heisenberg Central Products over Global Fields Smooth Diffeomorphisms and Mahler's Problem on Liouville Numbers Almost $k$-th powers in short intervals Exceptional points on Atkin--Lehner quotients Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function Distribution of Kaneko's val function A unification of Euler-Maclaurin and Euler-Boole summation formulas Improved bounds in Birch's theorem for forms in many variables Universal murmuration and Hecke augmentation Covering Projective Height Balls by Subspaces in Rigid Adelic Spaces Sharp lower bounds for shifted moments of Dedekind zeta functions Nonabelian Chabauty for the Thrice-punctured Line over Cyclotomic Fields An improvement on the largest prime factor of $n^2+1$ New classes of trace-form permutation polynomials and their compositional inverses Regularized spectral expansion of a Rankin--Selberg period and moments Confluence relations for $q$-analogues of multiple zeta values A General Construction of Codes from Drinfeld Modules On the Ramification of Quadratic Fields where there is a torsion growth A Proof of Fraenkel's Conjecture Ten unknowns for Hilbert's tenth problem over the integers The First Two Exceptional Boundaries for Sets with Few Subset Sums Shifted poles and chamber cancellation for classical Witten zeta functions Infinite transitivity of tame groups of automorphisms of affine spaces Hodge--Tate splitting and Akizuki--Nakano vanishing in positive characteristic Deciding superellipticity and computing the Weierstrass normal form Two-photon quantum Rabi models - Spectral degeneracy and symmetries On Algebraic Integrability of Vector Fields with Rational Function Coefficients that Separate Variables Sharp Threshold for Universality of Rational Canonical Forms over a Finite Field $A_1$ - Coulomb branches over finite fields and Selberg Character sums

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 variables Stable Solutions to Generalizations of Fibonacci Relations of Higher Order $q$-Analogues of some supercongruences related to generalized Van Hamme-type supercongruences Counterexamples to O'Neil's Period-Index Problem on Elliptic Curves Vanishing of $\mathrm{Sha}(A/K)[\mathfrak{P}^\infty]$ and its consequences for the anticyclotomic Iwasawa theory of $\mathrm{GL}_2$-abelian varieties The average number of rational preperiodic points of polynomials over $\mathbb{Q}$ Analogue of Cardy's formula on the 60-degree parallelogram: a modular approach The Shimura Lift and Hilbert Modular Forms Kato's main conjecture for nonordinary modular forms Lagrange spectrum for Diophantine approximations of complex numbers with real part equal to one half Luo's Spectral Large Sieve Inequality on Short Intervals Bloch-regulator Principal Parts of Cyclotomic Iwasawa Pseudomeasures On the special values of Berndt's generalized $L$-function Counting integral points near a curve in the n-dimensional Euclidean space Wallis-type products with polynomial exponents and the Dirichlet beta function at negative integers Exact logarithmic Hausdorff and capacity exponents of the non-Brjuno set Difference of the modular function $\omega_{2}(\tau)$, revisited Euler Characteristics of $\mathrm{SL}_4(\mathbb{Z})$ and $\mathrm{GL}_4(\mathbb{Z})$, and their cohomological consequences On supersingular isogeny graphs of Drinfeld modules The arithmetic of critical values II: critical elliptic curves Hecke 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 matrices Lower Bounds for Moments of $L$-functions Matrix representations and arithmetic properties of jacobsthal numbers via binary 3x3 matrices Sets whose differences avoid a bracket quadratic Complete characterization of a class of complete permutation quadrinomials over \(\mathbb{F}_{q^2}\) $13$ unknowns over quadratic integer rings and Lucas congruences Relative Langlands duality of the Bump-Friedberg-Ginzburg $\mathrm{GSO}_6$-integral Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces Unit Indices of Prime-Index Shanks Orders Density of the multidimensional Lagrange spectrum An Explicit Belyi Map for the Wiman Sextic and Cusp Forms for a Noncongruence Subgroup Reduced polynomial lifts of APN permutations over Galois rings and effective non-APN bounds Normal and Lognormal Asymptotics for Lattice-Point Counts in Random Translates of High-Dimensional Balls Counting solutions to quadratic forms in eight prime variables of off-diagonal rank $3$ Subconvexity of Short $k$-Free Exponential Sums in $\mathbb{F}_q[t]$ Large zeta sums and zeros of the Riemann zeta function Bounded gaps between primes Quantitative time-averaged spherical means along equidistributed spirals: Diophantine rates and limits of uniformity Lattice Green's function of the hyperkagome lattice: modular uniformization at level 30 from an orthogonal differential Galois group Flat connections on moduli spaces I: Local (1,0)-extension of the DHS connection Generalized Jantzen filtration, hyperbolic restriction, and characteristic cycles Pseudo-spherical representations and types for covers of split tori On the Babylonian Division of Trapezoids Recovering Laplacian Lattices from $L$-Functions of Graphs Prime and Touchard Congruences of Mixed-Type Bell Numbers A requested analytic proof of an identity of Dixit, Kumar, and Srivastava

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 Primality Finite and Symmetric Multiple $T$-Values Diophantine m-tuples of Triangular Numbers Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions An Erd\H{o}s-Wintner theorem for second-order linear recurrent bases The Multiplicative Persistence Conjecture: Resolving the \(2\)-Adic Obstruction for Nonzero Even Targets Drinfeld modular forms of higher rank from a lattice-oriented point of view Generalized Fermat equation over number fields Lattice points in high-dimensional $\ell^q$ balls with small radii Rational and integral values of rational functions at rational points Norm Principles for ${\rm Go}(q)$ and ${\rm Spin}(q)$ The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete Hypertori Rational torsion on simple genus two Jacobians Harmonic higher weight distributions, Simonis' approach of MacWilliams identity and moments Zero-free columns in character tables of symmetric groups On Frobenius rigidity for motivic cohomology On the number of $2$-dice games with prime power dice-size Arithmetic purity of strong approximation for toric varieties with constant global sections Betti bounds for spaces of curves on varieties and Manin's conjecture for quartic del Pezzo surfaces On Manin's conjecture for quartic del Pezzo fibrations

arXiv math.NTの新着論文30本をご紹介します。 番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-28/ Closed geodesics in homology classes modulo sublattices Discrete dynamics of Eratosthenes sieve $k$-Lucas Annulus for Polynomial Zeros A Neighbouring-Denominator Case of the Erd\H{o}s--Mahler Conjecture Period Relations for Theta Products and Elliptic Integral Moments The k-Rank Taylor Family: Canonical Harmonic Lifts, Principal Parts, and Rademacher Series $\mathbb{F}_q$-linear relations among Thakur's multiple zeta values in positive characteristic Torsion-vanishing for Siegel modular varieties via supercuspidal congruences Specialisations of the Burungale-Castella-Skinner main conjecture to $\mathbb Z_p$-lines Two-point correlations of multiplicative functions with dense orbits The Cartesian product of exact approximation sets Ap\'ery-type approximations and irrationality measures for certain $q$-series Resultants of dynatomic polynomials of $x^d$ Arithmetic purity of strong approximation for cubic hypersurfaces of large dimension Modular periodicity of the Euler up/down numbers at odd prime powers On variants of P\'olya's conjecture Exceptional covers of the projective line with genus-one Galois closure: arithmetic forms over finite fields The Matrix Pythagorean Equation over $\mathrm{GL}_2(\mathbb{Z})$ Birch's theorem over function fields with quadratically many variables On Consecutive Non-primitive Elements over Finite Fields On Piatetski-Shapiro primes from almost primes Integers divisible by a shifted prime in a given interval Delta theory of Anderson Modules II: Hodge-Pink structure Value distribution of multiplicative functions along linear fractional sequences On polynomial expanders with many variables Mixed Tate motives over number fields Isocrystals on unibranch varieties and open immersions The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\mathrm{GL}_n$ over Local non-Archimedean Fields Hankel determinants of Catalan-like sequences

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/2026-08-27/ On the sum of least prime factors in short intervals Transcendence of Tonelli--Shanks Power Modulo Infinitely Large Primes Jacob's ladders, new classes of sum variants of almost linear formula and corresponding $\zeta$-functionals and $\zeta$-equivalents of the Fermat-Wiles theorem The equality cases $P_t(\mathbb{N})=\tfrac12$ for the deconvolved sum-of-digits measures The uniform Littlewood conjecture fails on a set of positive Hausdorff dimension The divisor function for matrices Pseudonullity for fine Selmer groups over multiple $\mathbb{Z}_p^{d}$-extensions Simultaneous Diophantine approximation on the three-dimensional Veronese curve: the complete Hausdorff dimension story Well and badly approximable sets, and rapid winning An elliptic K3 surface X/Q(t) with Mordell-Weil rank 17, I: Formulas for X and base changes of rank 18 and 19 Rigid analytic 1-motives and conjugate uniformization of abeloid varieties Arithmetic theta invariants and arithmetic equilibrium measures A Short Proof of a Conjecture Regarding Quadratic Representations of Practical Numbers The Mixed Second Moment of Quadratic Dirichlet $L$-functions with Prime Conductors Intermediate-Range Estimates for Short Weyl Sums and Waring's Problem with Almost Proportional Summands A Boolean polynomial operator for the Collatz $3n+1$ problem The second moment of twisted modular $L$-functions and Dirichlet $L$-functions at the central point Sharp extremal asymptotics for Cusick's sum-of-digits bias at fixed Hamming weight Introduction to the Birch and Swinnerton-Dyer Conjecture An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms Remarks on Vafa-Witten theory, or how to sit on a wall A Categorical Framework for the Direct Integration of Banach Spaces

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/2026-08-26/ Collapsing Fifty Dilogarithm Arguments to Five Terms over $\mathbb{Q}\bigl(u,\sqrt{4-3u^{2}}\bigr)$ Poincar\'e duality in Hida families Fourier Spectral Reciprocity and Canonical Hecke $L$-Functions Geometric Realization of Finite Residue Casimirs and Weil Operators via Szeg\H{o} Kernels Sieve dimension and search depth for the Erd\H{o}s-Straus conjecture, $n \equiv 1 \pmod{24}$ Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals Winning property of counterexamples to Uniform Littlewood's Conjecture A Buium--Coleman bound for the Zilber--Pink conjecture for curves inside abelian varieties Sums of three powerful numbers Infinite continued fractions with a finite alphabet and their applications Polynomial representatives of finite-field maps: a sharp dimensional dichotomy Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups On the Geometry and Shapes of Rank 2 Log Unit Lattices Permutation and exceptionality of rational functions from equivariant elliptic isogenies over finite fields A dual reformulation of the complex sin^2-algorithm: exact identities, descent, and finiteness Contributions to the theory of the Euler eta function Integral quadratic forms over a ring of $p$-adic integers Weil positivity in compact windows: certified two-sided bounds and a Landau--Widom decay law Metaconjugation and Quadratic Forms Oscillation of partial sums of the M\"obius function and zeros of Riemann's zeta function Quantum Algorithms and Hardness for Point-Count Approximation over Finite Fields The Number of Curves of Genus 2 with a Given Refined Humbert Invariant Asymptotic Rounding Laws for Optimal Thresholds in Secretary Problems Kloosterman sheaves and Bessel functions for generic principal series of finite groups

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/2026-08-25/ A non-abelian large sieve and Artin's primitive root conjecture Rational Points and Brownian Motion Dense ascending waves: A resolution of the Alon-Spencer conjecture How many points has an affine algebraic set in residue classes modulo n ? Positive Logarithmic Hausdorff Measures of Exceptional Sets for the $p$-adic and $t$-adic Littlewood Conjectures General Stirling-Ramanujan Constants are exponential periods and applications Prime multipliers of order ten: norm spectra, local charts, and selective lifting Coherent sequences of matrix spectra A Classification of Small MSTD Sets in Arbitrary Fields A note on Zlobin's note Uniformity in rational torsion and small points on abelian varieties The strong form of Van der Waerden's conjecture via twisted Chowla The normalized approximation function for multiple zeta-star values Yun's zeta function and the overorder zeta function for Gorenstein cubic orders Kohnen--Ueda local newforms There and back again with Kaprekar 2-cycles On the constant in Klartag's theorem for lattice packings in high dimensions On uniqueness in equivariant Iwasawa theory Counterexamples to Dujella's conjecture on integral points on the elliptic curve attached to a Diophantine triple The Period-Three Secondary Term in the Mean Value of $L(1/2,\chi_D)$ in the Hyperelliptic Ensemble Cyclotomic norm congruences for zeta values and modular $L$-values Generically Ordinary One-parameter Hyperelliptic Families are Dense Orthogonality Defects of HKZ-Reduced Bases On the binary representation of powers of $3$ $p$-adic Equidistribution of Special Loci in a Product of Modular Curves Representations with k-generalized Fibonacci numbers Euclidean Rings A deterministic sin^2-type algorithm for complex cubic irrationalities with exact periodicity certificates Extreme values and logarithm laws for toral translations An elementary note on three consecutive powerful numbers On the graded center of $D(G)^c$ Quantitative Logarithmic Chowla Correlations Uniformly over Growing Shifts Power-saving bounds for Thue--Mahler and Mordell equations The classification of generalised Kummer surfaces in positive characteristic Admissibility of Bernstein centers Norm-Query Complexity of Algorithmic Problems in Finite-Dimensional p-adic Normed Spaces The Partition Pairing Theorems I MCSI: A Masked Commutative Supersingular Isogeny Key Exchange with Blinded Ephemeral Keys Marshall Quotients of the Rings $\mathbb Z/n\mathbb Z$ A motivic derived Fourier transform On the directions occurring in lattice-line coverings of the integer plane The asymptotic behavior of the rectangle partition function $p(m,n)$ An Exact Counting Formula for the Mutual Position of Two Plane Conics The Gao-Zhuang conjecture for the Heisenberg group The number of sum-free subsets of lattice cubes

arXiv math.NTの新着論文13本をご紹介します。 番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-24/ A note on least primitive roots Polylogarithmic Chabauty--Kim loci over number fields Maximal and minimal curves of the form $y^3=x^{(q^2+1)/2}+x$ Euler characteristic of the Selmer group attached to an Artin representation Complete Resolution Of A Family Of Twisted Thue Equations Arithmetic $\mathcal{D}$-modules over Laurent series fields: the relative case Adjoint Closures of Singular Pairs of Quadratic Forms and a Pfister-Type Criterion Legendre polynomials and complex multiplication, II: class numbers of quadratic fields and genus 2 supersingular polynomials Anabelian Geometry in Families Sums of products of Kloosterman sums to prime power moduli Almost sure upper bound for sums of random multiplicative functions and critical chaos On nearly consecutive sequences without long arithmetic progressions A new lower bound for two-color van der Waerden numbers

arXiv math.NTの新着論文21本をご紹介します。 番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-21/ Totally positive field extensions and the pythagorean index An Algebraic Approach to the Fundamental Theorem of Algebra Many Representations as Sums of Three Prime Cubes ${}_5F_4$ evaluations and a family of $\pi^2+\log^2$ identities On the Finiteness of Isolated $j$-invariants for $X_1(N)$ Quantitative bounds for sets lacking polynomial progressions with shifted prime difference Arithmetic partial differential operators on ramified extensions of $\ZZ_p$ Forced Shadows of an Obstructed Hyperbolic Kac-Moody Denominator Ribet Points, geometric divisibility sequence and order of reductions on semiabelian varieties The irrationality measure of arctan1/2 is at most 8.585166 Gap spectra and densities of slow Fibonacci walks Exceptional sets for compositions involving Euler's function,the divisor-sum function and Dedekind's function Simultaneous approximation to pairs of real numbers Modularity theorems for Eisenstein congruences in prime-power level Variation of Iwasawa Invariants for Ordinary Representations Simplex--center configurations in dense subsets of Euclidean spaces and the integer lattice On the number of solutions of systems of diagonal equations through diagonal GP-graphs: the general and the Hermitian-form cases Non-equivalence of pro-$p$-Iwahori invariants Spectrum of the refined Diophantine exponent The arithmetic de Rham stack The Local Langlands Correspondence for Middle Supercuspidal Representations of $p$-adic $\text{GL}(2n)$

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/2026-08-20/ On sums of two primes and six Fibonacci numbers Properties of Kloosterman sums for long Weyl element on GL(n) Rational Solids with Equal Surface Area and Volume Sharp Transitions for Localized Solutions to a Diophantine Inequality Mean Value Estimates for a Real-Exponent Analogue of Waring's Problem Asymptotics of Hecke polynomial coefficients on the Atkin-Lehner eigenspaces On $p$-adic solubility of $Ax^\ell + By^m + Cz^n = 0$ Hecke-type action on higher order Herglotz-Zagier function On the Diophantine Equation $p^x+ (2p+1)^y =z^2$ with Consecutive Exponents A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz Universal Ramanujan-type congruences for prime-detecting quasimodular forms The Position-wise Prime Digit Distribution Theorem: A Formal Proof of Position-wise Digit Equidistribution in the Prime Numbers On a classical zero-sum invariant Matchings and product growth in modular abelian independence groups On a conjecture on the Kasami APN function: reductions, structure theorems, a proof for $k\bmod n\in\{1,2,n{-}2,n{-}1\}$, and exhaustive verification for $n\le 13$ Finding suitably generic points on curves with an application to the construction of rigid real closed fields Spectral convergence of hyperbolic surfaces and quantum ergodicity Lonely Runners over Function Fields: Quantized Phase--Riesz product Products of trees and ${\rm PGL}_2$-torsors over the punctured affine line Complexity-sensitive additive energy and off-diagonal Young inequalities on bounded-degree algebraic varieties Eureka: Task-Conditioned Meta-Agent Orchestration for Scientific Discovery A simple construction of the automorphic residual spectrum A random walk on p-groups with a symmetric perfect pairing

arXiv math.NTの新着論文18本をご紹介します。 番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-19/ Prime-Exponent Transition Geometry and Divisor Barriers Between Consecutive Highly Composite Numbers Algebraic Lattices Arising from Congruence Submodules in Subfields of $p$-th Cyclotomic Fields Mild p-Class Tower Groups of Imaginary Quadratic Fields On Buzzard's Theoren Shifted second moment of Gaussian Hecke $L$-functions $L(s,\lambda^k)$ A central limit theorem for prime geodesics on random surfaces of large genus Ribet bimodules and principally polarized superspecial abelian varieties with quaternion action Alternating generalizations of Mizuno's product formula via modified gamma functions Infinitely many primes with a fixed Frobenius field for an elliptic curve over $\mathbb{Q}$ On the p-adic Wirsing problem On the integral $2$-adic Tate module of elliptic curves Principal nonsingularity of the Fourier matrices of orders \(70\) and \(143\) Intersecting families and nonvanishing multivariate polynomials over finite fields Squarefree polynomials with missing digits Products of point counts of higher genus curves over finite fields On the Hidden Pascal Symmetry and Moment Constraints of Vector Representatives in Quebbemann's 64-Dimensional Lattice Asymptotics of the Tchoukaillon array and a conjecture of Beluhov A Kernel-Checked Exclusion Certificate for Erd\H{o}s Problem 647

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/2026-08-18/ A descent-set obstruction for the Casas-Alvero conjecture Exponential sums over primes Reciprocity for The Short Twisted Second Moment of The Riemann Zeta Function Bounding The Number of Zeros Near the Central Point in Families of Cuspidal Newforms Transcendence of continued fractions over function fields and a quantitative version of Uchiyama's theorem Algebraic geometric framework of Rogers--Ramanujan identities Interlacing for zeros of the Serre derivative of Eisenstein series Positive quasimodular forms and the sign uncertainty principle Singular-weight Conway-invariant Jacobi forms of index four Proof of a Conjecture on Primitive Quartic Polynomials over Finite Fields Formal finite multiple zeta values Cycles of supersingular elliptic curves for pairing-based proof systems Beyond endoscopy for $\mathsf{GL}_2$ over $\mathbb{Q}$ with ramification 5: cancellation theory The principal series 2-representation for $\mathrm{GL}_n\times\mathrm{GL}_n$ over a 2-dimensional local field An exact formula for Erd\H{o}s' problem 1005 Hausdorff dimension of $\tau$-approximable points on self-similar sets in $\mathbb R^d$ Large values of quadratic character sums Better than square-root cancellation in Piatetski-Shapiro sequences Weighted singular vectors in common-base self-similar sets On the Hausdorff dimension of the difference sets between typical and normal numbers Height Rigidity for Entire Functions On integers that are representable as the sum of two units On the residual Eisenstein cohomology of unitary groups Simple and distinct zeros in a prime-modulus Dirichlet family at mesoscopic shrinking height Superspecial Points on Shimura Curves A dynamical generalization of Chowla's conjecture on average The multiplication table problem in large dimensions Oort's conjecture on supersingular abelian varieties in odd characteristic Subconvexity of Short $k$-Free Exponential Sums Galois descents of certain multiple polylogarithms M\"obius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications The equality between the Erd\H{o}s-Ginzburg-Ziv constant and the short product-one constant for finite nonabelian groups A six-functor formalism for syntomic cohomology Degrees of Genus-Two Split-Jacobian Loci and Humbert-Form Reconstruction Matrix group $\Lambda$-distributions

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/2026-08-17/ On the Existence of Hyperelliptic Curves over $\mathbb{Q}(T)$ with Certain Jacobian Ranks More than two thirds of the zeta zeros are simple and on the critical line Some Dwork-type $q$-supercongruences from a $_6\phi_5$ summation formula $p$-numerical semigroup of the sequence of consecutive odd integers A structural trace identity and certified spectra for the Richelot-Brandt graph A Kubilius model for sieve-theoretic sequences Ratio of sum of digits functions in two bases Hurwitz class number relations and mock modular forms New Congruences Involving $p$-adic dual sequences Shimura curves of discriminant 14 and 15 and associated Heun Functions The inverse Galois problem of iterated Galois groups and their fixed-point proportion Intensional semantics for comparison problems in arithmetic geometry Multiplicative chaos from random multiplicative functions Algebraic curves admitting automorphism groups of large prime square order Sharp refined-direction Kakeya estimates in finite Heisenberg groups Counting non-attracting subtrees and the equidistribution of repelling points Semi-abelian reduction of Albanese varieties Near diagonal additive energy bound for points on algebraic surfaces Compressive Domains and a Bound for the Number of Components of the Fixed Locus of a Self-Map of the Berkovich Line

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/2026-08-14/ On Waring--Goldbach problem with mixed powers Generalized Addition Theorems for the Jacobi Elliptic Functions A conditional arithmetic obstruction to the prime numbers as a spectrum of a probability measure Finding all cospectral mates over a number field Special Values of Shifted Dirichlet Series from an Adjoint Map on Almost Holomorphic Modular Forms Density bounds for permutations avoiding monotone arithmetic progressions Escalations and criteria over real quadratic fields Algebraic constructions of point sequences with quasi-uniform two-dimensional projections Uniform bounds on prime levels of abelian division fields of elliptic curves over number fields without rationally defined CM Finite-Sum Realization of Archimedean Asai and Exterior-Square $L$-Factors On the Lorenz-Fibonacci sequences and substitutions Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields A study of degenerate Bernoulli and Euler numbers via operators Analytic rank one propagation in Hida families On $\mathcal{B}^4$-almost periodicity for a class of arithmetical functions Generalizations of the Christoffel-Darboux formula and congruences involving Ap\'ery-like numbers Infinitely many elliptic curves over $\mathbb{Q}(i)$ of exact ranks 4 and 6 with $j$-invariant 1728 Asymptotic Analysis and Phase Transition of the Bessel-Kuznetsov Transform with an Oscillatory Phase On a conjecture of Corradi and Katai Convolution-type Bombieri-Vinogradov theorem with well-factorable Weights, and its applications Local Minkowski units in non-abelian extensions with cyclic Sylow $p$-subgroups Some convolution identities for mock modular forms arising from the theory of holomorphic projection Gross vectors modulo 2 and elliptic curves of prime conductor Intersective Polynomials and Universal Separation of Divosor Profiles The distribution of $k$-free ideals in ray class groups Multiplicative Subgroups of Prime Fields Are Not Sumsets The Five Distance Theorem For A Convex Norm Tame fundamental groups of rigid spaces Euclidean SVP is deterministically NP-hard to approximate within any constant factor Spectral and Isoperimetric Bounds on Flat Tori Optimal local convergence criteria for integer and Gaussian integer continued fractions

arXiv math.NTの新着論文18本をご紹介します。 番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-13/ The motivic Selmer scheme of the thrice-punctured line Upper bound for the moment of shifted values of cubic $L$-functions over function fields Galois Symbols for a Jacobian and Multiplicative Groups Equalities among simplest quartic fields: a complete classification Height lower bounds for elements of highly composite rings A $p$-part Birch and Swinnerton-Dyer Formula over Totally Imaginary Quadratic Extension of Totally Real Fields Hasse-Witt invariants for trace forms of Jacobi polynomials Duality formulas for $\widehat{\mathcal{Q}}$-multiple zeta values The 196560 auxiliary-function conjecture for the Leech lattice Multiplicator freeness for restricted-ramification Galois groups over global function fields Power sums and Siegel-type zero-free regions for L-functions A Multiplicative Fourier Proof of the Length-Four Index Conjecture On The Spectral Properties of Discrete Landscape Functions Visible Measures along $\Omega(n)$ and Distribution of Horocycle Orbits A Proof of a Conjecture on Fixed Perimeter Partitions Edit distance exponents for irrational rotations Invariant Functions on $p$-divisible Groups and the $p$-adic Corona Problem II Near optimal three-fold additive energy bound for points on convex curves

arXiv math.NTの新着論文16本をご紹介します。 番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-12/ On the Squarefree Values of Degree-$2q$ Polynomials An omega result for the first sign change of coefficients of symmetric power $L$-functions of Hecke-Maass cusp forms A proof of a weighted sum conjecture for finite multiple zeta values of level two Average root numbers in two isotrivial families of elliptic curves Permutation polynomials from the trace functions Bockstein Spectral Sequences and Applications to the Tame Fontaine Mazur Conjecture Distinguishing elliptic curves modulo $p$ and identifying images of product representations A canonical construction of signed $p$-adic $L$-functions for non-ordinary modular forms of weight $\leq p+1$ Equationless quadratic Chabauty for non-split Cartan modular curves A double-sum analogue of Whipple's summation formula and a restricted sum formula for multiple binomial sums Kneserized Anticoncentration and Reverse Absorption for Graham's Rearrangement Conjecture Classification of Fourier summation formulas on a horizontal strip Introduction to Universal Equations and Characteristic-free Resolution Mutation-preserving generalized cluster algebras and Laurent mutation invariants Finite monodromy groups in degenerating families and the stability degree of curves Poincar\'e \`a la Makdisi

arXiv math.NTの新着論文37本をご紹介します。 番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-11/ Zeta zeros of function fields heuristically equidistribute as genus goes to infinity Sharp vertex connectivity of the Markoff graphs modulo $p$ Positive Lower Density for Hofstadter's $ab-1$ Problem On the Emerton-Gee stack of potentially semistable representations Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures Which numbers are $u$-invariants of perfectoid fields? Binomial coefficients coprime to 6 Short Second Moment of $\mathrm{GL}(2)$ L-Functions via Trivial Delta Equidistribution for semiabelian varieties over number fields Machine-Guided Recurrence Boundary Theory for Nahm Sums On Sun's Conjectures for Truncated Jacobi-Symbol Determinants via Supersingular Elliptic Curves Proofs of the Conjectures on $SOME(n)$ and $DSOME(n)$ Functions Related to Integer Partitions The Mathieu group $M_{23}$ is a Galois group over $\mathbb{Q}$ A new hyperbolicity wedge and a joint semicircle limit for Jensen polynomials of Riemann's $\xi$-function Twisted Bernoulli Zeros in Quasi-Linear Time: Distribution, Depth, and Explicit Hilbert Class Components On some representations of Metacyclic groups whose integral forms can be computed from a single residual representation Modular resurgent structures for vectors Sharp Bounds for Rational Points Near Space Curves The minimal obstruction modulus for quadratic forms Plancherel and Poisson summation formulae for a family of affine $\Psi$-bundles A Sharper Explicit Result for the Sum of Two Almost Primes A proof of a conjecture on permutation polynomials An analogue of Hirose's relation for finite multiple harmonic $q$-series at roots of unity Counting metacyclic fields On the $\beta=2$ Partition function for Dirichlet $L$-functions in the $q$-aspect Large class of many-to-one mappings over quadratic extension of finite fields Uniform stratified vanishing and equidistribution on $\mathbb{G}_m^d$ On the Godement-Jacquet functional equation for finite matrix monoids The Borel complexity of non-Archimedean operator ranges Some new results for Andrews' Kimberling partitions Hankel Transform and $(\alpha,\beta)$ Somos-4 Sequences Jacobi Endpoint Pencils and Sharp Interlacing for Centered Binomial Samples A note on the partition function of a rectangle Restricted generalized Schur numbers Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages A proof of the cyclotomic conjecture and the non-existence of almost Moore digraphs Varieties with prescribed fundamental group schemes

arXiv math.NTの新着論文15本をご紹介します。 番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-10/ Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers Squarefree numbers in short intervals: explicit and formalized Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes A Combinatorial Approach to Vorono{\"i} Theory An extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for $\zeta_\mathbb{F}(2)$ and $\zeta_\mathbb{F}(2m+1)$ On semi-stable integral models for Shimura varieties Modularity of Higher Theta Series III: Proof of the Modularity Conjecture Towards the Fontaine--Mazur conjecture for GL(2) Heath-Brown identities for fractional powers of $\zeta$ On the Existence of Primitive Polynomials $f(x)=g(x)+ \lambda$ over Finite Fields Siegel zeros and small gaps between zeros of the Riemann zeta function $\Delta$-separated Sidon sets in additive number theory Universality for Random $p$-adic Polynomials and Random Matrices Via the Resultant Distribution Method A three-dimensional corner configuration involving the Omega function Arithmetic Properties of Mixed Stirling Numbers of the second kind