プレプリどんどん: math.NT

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 parts A new family of maximal curves not covered by the Hermitian curve Simultaneous nonvanishing of quadratic twists via Rankin-Cohen brackets Finite subgroups of outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields Norms of Schneider--Teitelbaum Polynomials in $p$-adic Fourier Theory Sampling and Moments of Reciprocal Quadratic Mellin Integrals On a question of Ruzsa about densities of sumsets A characterization of Sophie Germain primes - II The Three Gates: A Rooted-Operator Approach to Weil Positivity A problem of Yang and Chen on weighted representation functions Low moments of automorphic random multiplicative function sums Finding New Limit Points of Mahler Measure by Methods of Missing Data Restoration Computational results on sums of a prime with squares or cubes Rogers--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 sets On 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 fields Infinite prime sumsets in structured and $U^k(\Phi)$-uniform sets Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers I Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers II Logarithmic--exponential preparation in sharply o-minimal structures Combinatorics of hyperplane arrangements and Witten zeta function at the origin Morphism spaces on low degree hypersurfaces

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 Products Transcendence measure for the values of the logarithmic derivative of the Bessel function $J_0$ at algebraic arguments Lattice points close to a smooth curve and squarefull numbers in short intervals. II Effective Hecke eigenvalue equidistribution over the Atkin--Lehner subspaces Only finitely many modular Jacobians are supersingular modulo a given prime On two forms in many variables of different degrees Zero-Density Concentration for Dirichlet Polynomials Unramified Geometric Iwasawa theory of function fields Surjectivity of the Enots Wolley Sequence Continuous approximation to the reciprocal sum of the cubes of Fibonacci numbers Exact universal normalizations for the G\'al--Koksma lemma Nonvanishing of ray class $L$-functions A $q$-recurrence for a finite Ap\'ery limit Graded Algebras of Modular Forms and Sign Changes of Fourier Coefficients for Eta Quotients Bounded intervals containing a given number of primes Extreme Values of Quadratic Dirichlet $L$-Functions over Monic Irreducible Polynomials in $\mathbb{F}_q[t]$ Cyclotomic Prime Extractors Periodicity conjectures for all 2-sumfree sequences Extreme values of Euler-Kronecker constants of cubic abelian fields Stable Trace Formula for Newton strata of Shimura varieties On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result On a conjecture of Browning and Sawin on random hypersurfaces with sign coefficients A uniform effective Andr\'e--Oort result An Omega result for partial sums of the Riemann zeta function $\Omega$-results for the logarithmic derivative of $\zeta(s)$ on vertical homogeneous progressions Arithmetic Constraints and Limit Laws for Diagonal Rational Partitions Finite Fourier Duality, Radial Values, and Arithmetic of a Mod Eight False Theta Quotient Transcendence criteria for the minimal word of the rational base $3/2$ Tunnell-type criteria for variants of the congruent number problem Explicit equations of Galois subfields of Hermitian function fields with respect to decomposition groups The non-spherical sup-norm problem for $\mathrm{GL}(n)$ and generalized spherical functions Two proofs of the Cassels--Swinnerton-Dyer conjecture for cubic surfaces Generalized DCCQ: From Binary Quotients to Multinomial Simplex Geometry and Critical-Strip Coordinates On the singularities and the Kodaira dimension of unitary Shimura varieties A somewhat sure note on an un-Schur problem Graph lattice sums and graph zeta functions for long-range interacting quantum lattice models

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 Hypothesis Mean Lindel\"of Hypothesis and Prime Geodesic Theorem on Bianchi Manifolds A 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 $b$ entropy Elementary proofs of congruences modulo 5 for overpartitions with restricted odd differences Rational Points near Monofractal Curves and the Strong Oscillation Principle Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization Local Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrization Twisted Rational Zeros and Local-Global Principles for Linear Recurrence Sequences Higher Schwarzians of Elliptic Double Covers and Eisenstein--Kronecker Functions The Furstenberg-S\'ark\"ozy theorem for sums of an even number of odd powers An infinite family of imaginary biquadratic fields with a large class number Laurent series expansions for the Barnes multiple zeta function Triple divisor type functions in arithmetic progressions to prime power moduli Iwasawa theory of (directe) Cayley graphs The Local Ghost Theorem in the Tr\`es Ramifi\'e Case Distribution of squarefree integers with double congruence conditions Prime-power congruences for level-one eigenforms Extreme values of quadratic Hecke $L$-functions On $t$-sumfree sequences Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions in the level aspect An additive problem in connection with some quadratic real fields with class number one Powers of the Thue--Morse Series: 2-Adic Valuations and Automatic Odd Parts Refined conjectures on Fitting ideals of BDP Selmer groups Modular functoriality for finite groups Uniform Mordell-Lang conjecture for semiabelian varieties A class formula for effective Anderson motives On Sarnak--Str\"{o}mbergsson conjecture Improved bounds for Szpiro's conjecture Even-degree Hermitian Ikeda lifts via Fourier-Jacobi descent Hypothetical connection of the theta functions of Dirichlet characters with the real cyclotomic fields Loop spaces, twistor $\mathbb P^1$ and tempiric parameters List Decoding, Linear Hashing, and Furstenberg over $\mathbb{F}_q$ Block-count constrained harmonic sums: spectral expansion and block-directed Euler-Maclaurin On a classical zero-sum invariant II: Disproof of a long-standing conjecture Small degree isogenies between conjugate principally polarized superspecial abelian surfaces A perimeter analogue of Franklin's identity and an inequality related to the parity of parts

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-Conjecture Theta functions after Weil Dynamical uniform boundedness for unicritical polynomials and elliptic curves of large rank Arithmetic Siegel-Weil for the spherical Hecke algebra Galois representations and modularity for twisted moments of Kloosterman sums Pointwise ergodic theorems along sequences of intermediate growth Spherical statistics and phase transitions in high-dimensional lattices Finiteness of an Isogeny Class via Equidistribution Prime and Nonprime Totatives: A Sharp Construction and Exact Thresholds The optimal scale in Linnik's microsquare problem for almost all integers Generalized Wieferich primes and monogenic polynomials Density of Vanishing of Certain Eigenspaces of Cyclotomic Class Groups A Local Proof of Langlands's Second Main Lemma for Local Epsilon Factors over Nonarchimedean Local Fields Modular 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 digits Patterns in the Markov numbers and their generalizations Quantitative linear independence for square roots Twisted Lubin-Tate Big Witt Vectors and Fleck-Sun-Wan Congruences On Decomposition of Drinfeld cusp forms of level $t$ Golden-ratio growth of Conway's subprime closure Two-Height Approximation and Mahler's Problem on Liouville Numbers A Central Limit Theorem for Coprime Pair Counts in Randomly Translated Disks Surjectivity of Finite Rank-Capped Enots-Wolley Sequences The Jensen--P\'{o}lya program and inequalities for arithmetic sequences Cubic 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 covers An explicit power-saving bound for S\'{a}rk\"{o}zy's Theorem on shifted primes, assuming GRH Bloch cycles and the weak two-variable Chinburg conjecture Dynamical generalizations of Chowla's conjecture on short averages Elimination of Ren\'e Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem Asymptotic Formula for Biregular Overpartitions Critical Restricted Sumsets at the Boundary $\lvert A\rvert+\lvert B\rvert=p$ Prime Plus a Non-Square-Free Integer: An Elementary Approach Transcendence of Montgomery Reduction Factor in the Ring of Integers Modulo Infinitely Large Primes A proof of Sylvester's conjecture The typical size of Hecke eigenvalue sums is $o(\sqrt{x})$ Two-term dilogarithms, mixed-base Nahm sums, and Fricke symmetry Ekedahl-Oort strata meeting the supersingular locus Laurent coefficients of Zagier-type zeta function {\`a} la Ishibashi and arithmetic aspects of extended Ramanujan period function The Dynamical Mordell--Lang Conjecture for Relatively \'{E}tale Systems over Products of Curves On the largest prime factors less than $y$ of consecutive shifted primes Algorithms for $p$-rationality and for $p$-saturation of units Algebraic independence of the exponential and Weierstrass $\wp$-functions On the arithmetic of Tate-Shafarevich groups via Kolyvagin's conjecture Optimising Selberg's method for critical zeros On the number of solutions to $S$-unit equations Hecke structure of quaternionic modular forms mod $p$ Periodicity and Period-Length Bounds for Browkin $p$-Adic Continued Fractions An extension of algebraic independence of special values for non-lacunary power series Long runs of integers with small prime factors and the divisor function of $n!$ A Construction of an Extremal Even Unimodular Lattice of Rank $88$ Singular automorphic products and BKM algebras A septic covariant and the Hermite--Joubert problem in degree seven Another proof of the $U^4(\mathbf{F}_p^n)$-inverse theorem Cauchy laws for zeta logarithmic derivatives and stationary Stieltjes transforms Low moments of Hecke eigenvalue sums A lattice family with kissing constant $\tau(\mathcal{L}_n) \ge e^{\sqrt{n}}$ Zeros in The Character Table of The Wreath Product of The Symmetric Group Matrices over non-commutative rings as sums of fifth and seventh powers Subset-Sum Density Realization in Locally Finite Abelian Groups Torsion, Betti rank, and small points in semiabelian schemes Thresholds and Fluctuations for Colorful Arithmetic Progressions in Sparse Random Colorings Noether's problem for $A_6$ and $A_7$ Growth beyond exponent $3/2$ for convexity and iterated sum sets AKE principles in roughly deeply ramified henselian valued fields Algebraic Structures on Sets of Partitions NP-hardness of ideal lattice problems Geometric realizations of Brauer classes on K3 surfaces from hyperk\"ahler contractions Dynamical Mordell--Lang Conjecture for Higher-Rank Radially Ramified Skew Products

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 fields Local-global principles for visibility of lattice points on parameterized curves On the variation of slopes over moduli stacks of Galois representations Critical convergence and Hausdorff measures for generalized Flint Hills series $S_h$-sets in abelian groups A Generalization of S\'ark\"ozy's theorem in function fields Zeros of Quasimodular Forms Defined by Iterated Sums The first moment of quadratic Dirichlet $L$-functions in the even hyperelliptic ensemble Tight universality of $m$-gonal forms with minimal criterion sets Gauss Genus Theory in Characteristic 2 Projective Kernels and Replicability in Modular Function Theory Classification of torsion of elliptic curves over quintic fields Large fluctuations of extended Rademacher random multiplicative functions Projection and fibering in groups of bounded exponent Kronecker sequences beyond the torus: nearest-neighbour distances and best returns Iwasawa theory of CM elliptic curves at potentially supersingular primes Kolyvagin's conjecture at non-ordinary primes An asymptotic formula for a cubic moment of $GL_2$ $L$-functions Jacquet--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 Fraction Serre's problem on statistics of Brauer symbols Poincar\'e duality for pro-\'etale $\mathbf{Q}_p$-local systems Characteristic Classes of Adelic Vector Bundles and Applications Non-archimedean Monge-Amp\`ere measures for toric metrics on subvarieties of toric varieties

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 Integers Sums of distinct divisors of factorials Ordinary 3-Isogeny Graphs and Improvement of Supersingularity Testing for Twisted Hessian Curves over Prime Fields Effective estimates for exponential sums with multiplicative coefficients Rational Approximations for Reciprocals of Multiple Zeta Values and Trivariate Cauchy Numbers A $p$-adic monodromy theorem for curves Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals Log-crystalline representations and $(\varphi, \Gamma)$-modules The irrationality measure of {\pi} is at most 7.101862832357 On the bounded-conductor finiteness conjecture in equal characteristic Sharp unconditional moment bounds for products of L-functions Internal congruences modulo powers of $2$ for overpartition tuples with odd parts Generalized Frobenius Partitions Modulo Powers of $2$ Bounded asymptotic bases for linear forms Chowla's non-vanishing conjecture over $\mathbb{F}_q(T)$ The asymptotic in Waring's problem over function fields beyond twice the degree On the Mahler measure and root distribution of the $Q$-polynomial of links The 2-Adic Valuation of the Order of the All-Ones Class in the Sandpile Group of a Square F-theory on K3 surfaces and orthogonal modular forms A dynamic point of view on universality for random matrices over finite local rings Quantitative universality for products of i.i.d. random matrices Rankin--Selberg integrals of opposite conductor--one newforms Divisibility and torsion in higher Chow groups over arithmetic fields Reversibility and its asymptotic counting in Picard group A maximal function field of genus $17$ over $\mathbb{F}_{11^2}$ Cusp restrictions and Bunke--Naumann invariants with level structure

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 conjecture The density of long runs of non-$r$-free integers Spectral Algebras of Abelian Cayley Graphs Triple intersections for algebraic curves on the real torus Cyclotomy of symmetric polynomials Effective Euler Sums The addition on totally positive integers uniquely determines the totally real number field Generic Manin-Mumford Regular Arithmetic Functions, Volume I. Theory, Applications, Examples What Does MMLU Actually Measure? A Psychometric Audit of Difficulty Structure in Aggregate Benchmark Scores Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny Integer group determinants for the elementary abelian group of order 49 The three Kanade-Russell identities modulo nine From Pythagorean Runs to Pell-Generated Cubic Runs An elementary approach to Sun Kim's general theta function identities Universal norms and de Rham representations Unramified Motivic Alternating Multiple Mixed Values Non-vanishing of symmetric square $L$-functions in the weight aspect Pencils of norm form equations and a conjecture of Thomas, II Diophantine approximation with primes in an arithmetic progression A 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 fields Faltings' Isogeny Theorem via Equidistribution Quasi-modularity of symmetric quasi-shuffles Sharp local estimates for smooth numbers On the syntomic regulator of the Hesse cubic curves and $p$-adic hypergeometric functions Integer group determinants for abelian groups of order 24 On the Number of Hecke Eigenvalues of Same Sign on $\mathrm{GL}_n$ Irreducibility of truncations of the Catalan generating function $B_h$-sets and perturbations in normed vector spaces The algebraic geometry of 3-by-3 magic squares of squares Positivity and Asymptotics for Chenevier's Orthogonal Polynomials Distinguished standard modules for $\mathrm{GL}_{2m}(\mathbb{C})/\mathrm{GL}_m(\mathbb{H})$

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 theorem On the Diophantine Equations Arising from Three-Term $b$-Concatenations in Pell-Type Sequences Primes with Restricted-Digit Differences On the classification of small cyclotomic integers On the class number of certain cyclotomic fields A $q$-microscope for mock-theta denominator patterns Infinite-order $p$-adic differential equations for Hurwitz-type Euler zeta functions: Higher-dimensional extensions and uniqueness of bounded solutions The entropy of coclass one and of SmallGroup(729,45) Central non-vanishing of Dirichlet $L$-functions From dimension four to dimension five in the Tate conjecture for abelian varieties over finite fields Lattice point visibility along polynomials has density one Normal Behavior and Periodic Points of a Pseudo-Aliquot Map Associated with the Dedekind Psi Function Mean Values and Normal Order of a Successive-Iterate Ratio of Dedekind's Arithmetic Function Bounds on Whittaker Functions for $\mathrm{GL}(n)$ Fields of definition of $p$-torsion points of elliptic curves and their ramification Methods to Find Integer Points on the Elliptic Curve of Factorizable Polynomial Equation Optimization of Quadratic Sieve Algorithm Implementation for Large Integer Factorization Unsupported Cyclotomic Divisors in Three-Prime Integer Tilings Generalized Zeckendorf expansions of the 2nd order A Fricke transformation for cubic-residue eta products of level 13 High dimensional Riemann--Roch spaces in linear spaces with small squares Three 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 functions Upper bounds for arithmetic functions over polynomial values via Chebotarev--Sato--Tate distributions The method of telescoping continued fractions Counting Representations of Quadratic Forms A Proof of Bala's Congruence Conjectures for A158690 Parameterized partial theta identities and a unified $q$-difference proof The Normal Form of Smith's Matrices On a problem of Nathanson related to minimal asymptotic bases and maximal asymptotic nonbases Prime pairs along rays of prime indices On Dynamical Mordell-Lang Conjecture for Split Map Asymptotically optimal packings of arithmetic progressions with prime differences $\vec M$ Versions of Andrews-Gordon Identities Revisited Zeros of Ramanujan-Like Polynomials Residual finiteness and cuspidal cohomology of Picard modular surfaces Sharp Diameter Bounds for Nonnegative Cyclotomic Multiples A pencil of quadratic forms in nine variables with no member of Witt index four The spectrum of $(\xi\alpha^n)$ can be uncountable Equidistribution of small points over finitely generated fields The Artin-Hasse $p$-section: weighted convolutions and $p$-adic recovery Simple critical zeros and distinct zeros of the Riemann zeta-function in short intervals The Fibonacci numbers are not an additive uniqueness set for multiplicative functions Relative $(\varphi, \Gamma)$-modules and $p$-adic differential equations A Lang-Trotter Problem for Non-Geometric Quadratic Inductions Replication Descent and $J$-Finality of Replicable Functions Todd's relation conjecture and binary relations for multiple zeta values in positive characteristic Pascal tiling and congruences modulo N in Pascal's triangle Moments of the Crank Statistic for $t$-Core Partitions and Overpartitions Prescribed Abscissae on Congruent-Number Curves over Simplest Cubic Fields Second derivatives of $p$-adic $L$-functions and the Shafarevich--Tate group of rank-two CM elliptic curves Counting Survivor Sets: Exponential Equivalence with Prime-Admissible Sets Symmetric power L-functions of a weighted hyper-Kloosterman family A geometric Jacquet--Langlands correspondence for Shimura varieties Four explicit continued fractions for values of the Lerch transcendent and the Hurwitz zeta function A Problem on the largest divisor $d$ of $N$ with $d\leq \sqrt{N}$ Reduction Modulo Binary Polynomials with Logarithmic Feedback Depth On a problem of Erd\H{o}s and Nathanson related to minimal asymptotic bases of order $h$ On the cardinality of the exception set in Littlewood's discrete conjecture Generalizing a Pair of Diophantine Equations The modulo 9 Kanade--Russell identities and their Nahm-sum duals Rational functions over finite fields with Galois closure of genus zero Sharp order-preserving integer models for short additive equalities The Archimedean place is a blurred interval at infinity Coarse moduli of motivic augmentations Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers Polynomial point counts for moduli spaces of curves with marked points The Constant in Thomae-Type Formulas for Eight Points on the Complex Projective Line Microlocalization and singular supports of constructible \'etale sheaves A Uniform Product-Difference Theorem for Dense Subsets of $\mathbb Z^2$ External Difference Families Arising from Two or Three Cyclotomic Classes The exponent of harmonic LCM avoidance Solutions to 6 problems in recurrence and Van der Corput sets Logarithmic $A_{\mathrm{inf}}$-cohomology, Part II Proofs of Some Kanade--Russell Mod 12 Conjectures Majorization and additive tuples in $\mathbb{Z}_2^n$ A Perfectoid Pro-\'Etale Lie Torsor Can Have a Non-Surjective Sen Map On the $a$-number of Fermat type function fields and some of their subfields The range and omitted values of a certain sequence involving the partition function The sharp constant in the Mashreghi-Ransford inequality

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 $\lambda$-rings SIC dimension towers via cyclotomic polynomials A counterexample to the Chung-Graham-Spiro gap-set conjecture Hilbert's Irreducibility for $\mathbb{G}_m$ Degeneration of monodromy in the theory of Eisenstein congruences for classical groups Numerical experiments on the Hardy conjecture for the Gauss circle problem On multiply induced characters On the Divisibility Relation $\sigma(n)\mid\sigma(n+h)$ and a Generalized Erd\H{o}s--Sierpi\'nski Conjecture Distribution properties of generalized polynomials The Right Edge of the Zero Set of the Fibonacci Zeta Function Lattice point visibility along powers of quadratic polynomials The Prouhet--Tarry--Escott problem for subsets with small doubling in integral domains Counting level-raising congruences using modular representation theory Local Jacquet-Shalika integrals and modifying factors Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions F-sets of arbitrary finite width Distribution of points near the origin in the $d$-dimensional Lagrange spectrum Short arithmetic terms express the cardinality of elliptic curves in Weierstra{\ss} normal form over finite fields Cone upgrade for effective equidistribution and weighted Khintchine--Schmidt theorem on fractals Coleman Isomorphisms in Syntomic Cohomology and $\mathrm{THH}$ A Log-Free $n^{1/5}$ Bound for Chowla's Cosine Problem Arithmetic Polyhedra Counting sets with given doubling via dimension

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 $\text{GL}(2n)$