プレプリどんどん: math.NT

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 rationals Mixed moment and joint non-vanishing of $\mathrm{GL}(3)\times\mathrm{GL}(1)$ and $\mathrm{GL}(1)$ $L$-functions Ehrhart 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 Formula A simpler proof that there are no Landau--Siegel zeros Optimal Reduced Representatives of Quadratic APN Permutations in Odd Dimension Explicit reduced APN permutations: ramification and optimal Galois-ring lifts Non-vanishing mod $p$ of derived Hecke algebras of multiplicative groups over number fields, II Modularity criteria for multiple Eisenstein series On the dimension conjecture for global Galois deformation rings in characteristic two Smoothness of Shortest Isogenies to Frobenius Conjugates Imaginary quadratic fields of class number at most 2000 Frey-Mazur theorem for semistable elliptic curves over function fields Local Tate duality for syntomic cohomology in positive characteristic A prime plus a square: A conditional 11/20 upper bound A New Bound for the Gauss Circle Problem A number field extension of Ramanujan's identity and its integral representation via the generalized Riemann $\Xi$-function Twisted Artin-Schreier Theory I: $(C_p \rtimes C_{p-1})$-extensions of local function fields Isaac's Condition (TU) is false A variation on local trilinear form An introduction to algebraic groups On the Sampling of Certain Dirichlet and Prime Sums at Gram Points and their Viscosity Classification of vanishing fusion rings of rank four Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties Logarithmic exponential sums with multiplicative coefficients The discrete second moment of the Riemann zeta-function along powers of Gram points Variation of Shafarevich-Tate groups in Hida families Automorphic Dirac Operators and an Analogue of the Quantum Harmonic Oscillator on $\Gamma \backslash \mathfrak{H}$ On exponential sums with multiplicative coefficients A counterexample to a conjecture of Plotnick on knot exteriors Local Extrema and Infinite Derivatives of the Delange Function of Base 3 Density of repelling periodic points for cubic rational maps Generalized Erd\H{o}s--Ginzburg--Ziv Constants for finite abelian groups of rank three The $L\log L$-Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of Dimensionality B\'ezout bounds and rational points on quasianalytic graphs An undecidable problem in dynamics Unimodular Zeros of Selmer's Harmonic Trinomials Double covers of tori for p=2 and genuine functions

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 recurrences Large value estimates for Dirichlet polynomials and trilinear sums over short intervals Orthogonality relation between $GL(3)$ coefficients and additive characters with linear and non-linear phases Some Bounds on the Lehmer Index Elliptic curves attached to Jacobians with imaginary multiplication A new way integral for the $n$-fold cover of $SL_2$ An algebro-geometric approach to profinite iterated monodromy groups A Bounded-Defect Construction for the Mondrian Art Problem Reductions of Galois representations of slope $2$ Zero-cycles and Brauer groups on certain Enriques surfaces Ternary polynomial relations and periods of cusp forms Shapes of tame abelian number fields A folklore conjecture on multiplicative exponential sums Arithmetic Visibility in Polygons: Curved Sight in the Art Gallery On a problem on partitions into distinct primes The Density and Quantitative Upper Bound of Integers Not Expressible as the Sum of a Prime and a Zumkeller Number On the Erd\H{o}s--Odlyzko--S\'ark\"ozy conjecture for prime-power moduli Divisibility Estimates for Gaussian Norms and Almost-Prime Orders of a CM Elliptic Curve Primes between 8th powers? Conguences for Odd Unimodal Sequences and a Problem of Bringmann And Lovejoy Integral Specializations of Polynomials: Hilbert Irreducibility, Coprimality, and Density New bounds for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ shifted convolution sums Genus character $L$-functions of orders in quadratic function fields On the Hardy--Littlewood--Chowla conjecture An upper bound for valuations of elliptic nets at primes of bad reduction Quantitative lower bound for Pythagorean pairs in boxes of prime powers S-squareful values of binary quadratic forms GCD and ABC inequalities for abelian varieties over function fields Universal norms of partially de Rham $B$-pairs and perfectness in Lubin--Tate Iwasawa theory The large sieve inequality and additive decompositions of sums of squares Arithmetic Siegel--Weil formula on the product of modular curves The existence of small defining polynomials for number fields $\ell$-Independence, slopes, and weights of $\ell$-adic cohomology groups of rigid spaces Symplectic extension graphs and Ribet's lemma Positivity and negativity for $h$-bases for $n$ Proofs and disproofs of some conjectures on zero-sum problems of new types Reciprocal Dynamics in Congruence Jumping: Integral Orbits and Valuation Cones A prismatic Riemann-Hilbert correspondence Effective equidistribution of polynomial trajectories in $\operatorname{SL}_3(\mathbb R)/\operatorname{SL}_3(\mathbb Z)$

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-heights Geometric bounds on norms of signed indecomposable integers Wendt's determinant and finiteness of prime characteristics for permutation binomials Linking numbers and special differential characters in arithmetic hyperbolic manifolds Some applications of the quasi-Riemann hypothesis to class groups and small generators of number fields On Permutations Whose Adjacent-Sum Reciprocals Sum to One A Combinatorial Proof of Partition Identities for the Number of Distinct Part Sizes Untrodden pathways in the study of partitions with parts separated by parity Higher rank elliptic sieve via CM endomorphisms Counting matrices with given characteristic polynomial A certified classical-strip comparison for the de Bruijn-Newman constant On Berndt-Straub conjectures about zeros of generalized Ramanujan polynomials A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral ${}_2H_2$ summation Fine structure of even Galois deformation rings A recurrence in logarithmic M\"obius sums with coprimality conditions via Euler--Maclaurin Yau's number-theoretic conjecture and sharp spectral bounds for quantum harmonic oscillators A sharp lower bound for the sextic large sieve Simultaneously preperiodic points and colliding orbits for families of polynomials in characteristic $p$ The local structure of refined class groups in cyclotomic Iwasawa theory Roth's theorem on weighted projective lines Proofs 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 Polynomials Proof of a nonnegativity conjecture of Prellberg--Stanton Integral trace duality and the Witt filtration on Lubin--Tate space Moduli descriptions of v-sheaf local models Hyperelliptic curves on $K3$ surfaces Higher derivatives of the Gram function Arithmetic jet spaces and the unramified Zilber--Pink conjecture for subvarieties of abelian varieties Denominators in the Farey Sequence, the Stern Sequence, and the Frobenius Problem with Relatively Prime Multipliers Likely and unlikely ramification of algebraic points on curves An Enhanced Higher Green's Function on the Modular Curve Holonomic sequences arising from meromorphic modular forms A Half-Constant Upper Bound for Chowla's Cosine Problem Distribution of central values of Hecke $L$-functions of $n$-th order characters CM fibers of Shimura parametrizations and thirteen proofs of the class number one theorem The WZ pair and finite congruences Automorphisms and canonical forms of integer lattices On Solvable Automorphism Groups of Function Fields over Finite Fields Pointwise improvement of the error term in the higher rank hyperbolic lattice counting problem Sparse Lifts of q-Linearized Permutation Polynomials with Explicit Inverses The ring of values of $E$-functions is not a field The Davenport constant of low-dimensional boxes Bounded continued fractions and quadratic orders in $\Q(\sqrt{127})$ Hecke modules associated to certain even ternary lattices of half-discriminant $\mathbf{N^2}$ Stable reduction and large Nielsen orbits on generalized Markoff surfaces Dynamical generalizations of the two-point Chowla conjecture A Lean formalisation of the disproof of Ramaekers's conjecture Irreducible components of crystabelline deformation rings: the wildly ramified case Wasserstein rates of all orders for the Sato-Tate law of Kloosterman sums Cohen-Lenstra heuristics and vanishing of zeta functions for superelliptic curves over finite fields The Multiplicity One Defect and Congruence-Modular Exponent Ratios Low Lying Zeros of Dedekind Zeta Functions On bass orders in division algebras Square integrable representations and Hecke eigenvalues over a local non-archimedian field Privileged $\mathrm{SL}_3$-local systems are motivic p-adic Hodge theory of unipotent completions revisited Cyclotomic Structure and Exact Recurrences in Floquet Many-Body Quantum Dynamics Microlocal Arthur packets as a quasi-canonical basis of stable distributions The weak cylinder conjecture for polynomial graphs of bounded degree Galois coinvariants and fundamental groups of arithmetic schemes $2$-large sets are sets of nil-Bohr recurrence Depth-zero local Langlands via shtukas in mixed characteristic Nonarchimedean discrete groups and quasi-isometric doubles of free groups Cubic moments of eigenfunctions on surfaces Zero density in short strips and short-interval bounds toward Hypothesis S Nonlinear twists of Rankin-Selberg coefficients in the eigenvalue aspect Iwasawa cohomology of pseudorigid families of $(\varphi,\Gamma)$-modules A note on the $p$-adic inhomogeneous Littlewood conjecture $6$ powers of $2$ in the Linnik--Goldbach problem Tribonacci numbers that are palindromic concatenations of two distinct repdigits On the inverse Goldbach problem Solutions of $x_1^2+x_2^2-x_3^2=D$ with small $x_3$: a spectral approach Poissonian Pair Correlation for Bernoulli Orbits Counting subspaces with prescribed Welch sums Coprime pairs with equal sum of divisors, assuming smooth shifted primes Bloch torsion and modular combinations of Nahm sums The Goldbach exceptional set: an exponent 7/12 and conditional refinement A linear independence criterion for $p$-adic Hurwitz zeta values at odd integers On the OpenAI proof that Landau-Siegel zeros do not exist On strongly minimal asymptotic bases of order $h$ generated by powers of $2$ Monotonicity of Coefficients of Interpolated Multiple Zeta Values Non-vanishing of primitive cubic, quartic and sextic L-functions Counting Rational Points on a Certain Bihomogeneous Threefold Refining the 7/8 zero-free half-plane for Hecke and Dirichlet L-functions The Norm Spectrum of Barnes-Wall Lattices Below Twice the Minimum Bernoulli numbers and the integer group determinants of $C_p \times C_p$ Post-critically finite polynomials over cyclotomic closures of number fields Universal Shift Congruences for Weighted Permutation Sequences Post-critically finite polynomials in characteristic $p$ Crystals and the parabolicity conjecture A trace Paley-Wiener theorem for $\mathrm{GL}_{n}(F)\backslash \mathrm{GL}_{n}(E)$, with $E/F$ a quadratic extension of non-Archimedean local fields Deformation and Symmetry in Two Hypergeometric Supercongruences A quotient of the Bruhat-Tits building classifying maximal matrix orders over curves On Waring-Goldbach problem for two squares, three biquadratics, one quintic and one septic On a variant of the Piatetski-Shapiro prime number theorem Kitaoka's conjecture for real cyclotomic fields Proof of Two Conjectural $q$-Supercongruences Related to Van Hamme's $\mathrm{(G.2)}$ Supercongruence Exact Rank of the Largest Good Lattice Point Matrix Bounds for (k,c) model functions over p-adic fields Examples of Bessel Functions of Order Zero Related to the Functional Equation of the Riemann Zeta Function On trace-zero norm forms of orders of rational quaternion algebras with applications Simultaneous Unimodularity of Positive Integer Matrices and Their Entrywise Cubes Sharp Constants and Extremizers in Homogeneous Tree BMO The strong Ramanujan bound for Drinfeld modular forms On the generalization of Christol's theorem to domains of finite type over finite fields Polynomial Identities for Generalized Fibonacci Sequences How iterated sumsets grow under the assumption of small doubling Overlap distributions under the Gibbs measure of a Haar model of $\log|\zeta|$ on and near the critical line Survivor Set of Gauss Map with a Hole at $1$ Bounds for the residue of Dedekind zeta functions under GRH and applications On the calculation of an integral introduced by Hubert Delange A lower bound for additive complements to the primes Lattices with Large Kissing Number from Local Density Schauder and Riesz Bases for Higher-Dimensional Lebesgue Spaces Inspired by ReLU Neural Networks A series with a Cantorval set of subsums and ratio of consecutive terms tending to $1/2$ (the second Jones problem) Dynamical degrees of automorphisms of non-projective hyperk\"ahler manifolds Uniformly Bounded Orthonormal Bases of Homogeneous Polynomials on the Complex Sphere

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 fields Properness of the Cuspidal Hilbert Eigenvariety A cyclotomic gluing construction for lattice sphere packings Hankel Matrix Decompositions and Digital Sequences over Function Fields Polynomial parametrization of $\text{SL}_2$ over global function field rings A Rigid Analytic Curve Can Have a Dense $p$-adic Orbit A conditional bound $\Lambda\le0.13963$ for the de Bruijn--Newman constant Reciprocal LCM powers and Robin's criterion Reasonable 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 rectangles Product and Quotient Set Dominance in Finite Groups On Quadric Surfaces Weighted by Arbitrary Coefficients Hecke Eigenform Product Identities for Full-Level Hilbert Modular Forms The order types of the supports of $p$-adic algebraic Hahn series Stieltjes constants for Hurwitz-type L-series attached to periodic arithmetic functions Towards linear growth for biprojective hypersurfaces of small dimension Real Fiducial Vectors Only Exist in Dimensions $d\equiv 3 \pmod{4}$ On the Quantitative Bounds of Nonlinear Roth Theorem Hecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$ Short Recurrences and Straight-Line Programs for Primes Sharp Bounds for Limits of $N$-Point Correlation Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of $(-1)^{\omega(n)}$ On a conjecture on Romanoff type representations On Divisor Function Polynomials and Dirichlet Series On the saturability of $p$-adic Lie groups An Infinite Family of Ap\'ery-like Recurrences for Euler's Constant Covering plane curves over finite fields with lines Khintchine dichotomy for images of self-similar measures and almost random walks Higher mod $p$ Satake transforms: explicit formulas and images for $\mathrm{GL}_2$ Thurston's Legacy at the Interface of Surface Dynamics, Train Tracks, and Arithmetic Campana strong approximation on generalised Markoff surfaces Weighted, GIT and N\'eron--Tate heights on genus-two moduli and Jacobians Counting with Hiccup Sequences The Tate Conjecture for Ordinary Calabi-Yau Threefolds

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 quotients Logarithmic moments of the Rogers Ramanujan continued fraction and odd zeta values Multiplicity Constants for Rough Numbers in Prime Gaps Finite-radius Jensen and relative-entropy formulations of the Balazard--Saias--Yor criterion Simple and accurate approximations to Dirichlet $L$-functions A Generalization of the Riemann Functional Equation with Three Variables Irreducibility of Generalised Laguerre Polynomials for Large Integer Parameters Classification of the Orbits of Three Quadratic Collatz-type Maps Simultaneous non-vanishing of twists of $\mathrm{GL}_3$ and $\mathrm{GL}_1$ $L$-functions Long intervals of consecutive composite values of polynomials Cardinalities of Jordan Diophantine sets of upper triangular integer matrices Non-degeneracy and Fibering with Applications to Diophantine Approximation Equidistribution of number theoretic point sets in the torus and the sphere in Wasserstein metric and $L^2$ discrepancy Splitting fields of complex hyperbolic groups: matrix extraction, Hermitian descent, and spectral fields Additive Sums of Generalized Shifted Ternary Divisor Functions A note on Riemann's $R$-function and almost primes A combinatorial proof of the quadratic Gauss sum Horizontal moments of Kloosterman sums and a density version of sieves Automorphic symbols and automorphic \emph{L}-values of GL(2) over imaginary quadratic fields Statistics of divisor functions over function fields Ray class monoids for orders of number fields Weak and genuine A_n-formality for number fields Invariant Measures on Smooth Algebraic Groups over Higher Local Fields Discorrelation of the M\"obius function with linear phases in short intervals New Hoffman-type generators for alternating multiple zeta values A Unified Framework for $p$-adic Congruences and $p$-adic Interpolations of Sequences $q$-Supercongruences Modulo the Third and Fifth Powers of a Cyclotomic Polynomial $q$-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruences Uniform Height Gaps in Arbitrary Characteristics Pythagorean pairs in boxes of prime powers Uniform non-vanishing of prime quadratic twists of standard and symmetric square $L$-functions Unipotent Selmer dimensions for CM curves via Iwasawa loci Further bounds in the polynomial Szemer\'edi theorem Hyperplane winning for bad in manifolds A uniform bound for the minimal degree of an isogeny between principally polarized superspecial abelian surfaces Geometric families of multiple elliptic Gamma functions and arithmetic applications, III On $a^4+b^4+c^4+d^4=(a+27(b+c+d))^4$ and ten other new infinite families On Igusa's conjectures for weighted homogeneous polynomials with isolated singularities Slightly improved zero-free half-planes for the quasi-Riemann hypothesis Two Primes and Five Mixed Fibonacci-Lucas Summands Geometrically Abelian Sections on Higher-Dimensional Varieties The Erd\H{o}s-Falconer distance problem in the integer lattice K-Moduli Wall Crossing and Automorphic Forms for the Moduli Space of Rational Elliptic Surfaces K-moduli wall crossing for quasimaps to a projective variety Continuity of the Julia sets in non-archimedean and hybrid settings On the asymptotic behavior of the number variance of random points on the unit torus Arithmetic Progressions in Midpoint Colourings Largeness of the wild locus Rational curves on toroidal compactifications of Picard modular varieties A Complete Proof of Mueller--Ho Conjecture Twisted Jacquet modules and induction from Speh representations

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 Primes Consecutive Cycle Sums More than 83.9% of the zeros of the Riemann zeta function are distinct and more than 67.35% are simple and on the critical line Automorphisms of general modular curves Affine Coordinate Subspaces and Strong Khintchine Convergence Idempotence in Carmichael and Giuga numbers and its application to the Agoh-Giuga conjecture On a Digital Signature Based on Matrix Decomposition and the MinRank Problem On 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 Pappas Higher order uniformity of the primes and cancellation of the M\"obius function in shorter intervals Prime points on smooth hypersurfaces Linear independence of values of polylogarithms with periodic coefficients, outside the disk of convergence Maximal volume of convex bodies avoiding random points and lacunary dilates Translation-invariant equations in $\mathbb{F}_p^n$ and groups Terminal Blocks of Primes in Pisot Numeration Systems Spacing statistics for a point scatterer on the cubic three-torus Consecutive Rankin-Cohen Bases, Full-Spark Periods, and Divisor-Tau Congruences Invariant Primes in Lubin-Tate Space and Hovey-Strickland at Every Height Generating sets for maximal orders in rational quaternion algebras Improved average and almost-all bounds for $G(n)$ Irrationality exponents of logarithms of positive rational numbers Intersecting a curve in an abelian variety with multiples of another curve Local Factors in the BSD Conjecture: A Unified Statistical View Cocycle Relations and Elliptic Gamma Values Mixed moments of arithmetic functions and Kloosterman sums $p$-class groups in the cyclotomic $\mathbb{Z}_p$-extension of imaginary quadratic fields Equivariant Unirationality of Cubic Threefolds Making Every Number from 1 to N Under a Fixed Cycle of $+$, $\times$, $-$, $\div$ Points and their multiples on curves in powers of simple abelian varieties

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 Fields CUDA-MPQS: A GPU-Resident Self-Initializing Quadratic Sieve, and the Factorization of RSA-155 On the class number of real multiquadratic fields The 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 sequences On eutactic forms Lifting ethereal Bianchi modular forms Gaps theorems for linear forms with cubic coefficients Further results on the paramodular Hecke algebra Primitive normal progressions in finite fields A new bound for the Furstenberg--S\'ark\"ozy theorem using the van der Corput property Carlet's cyclic-additive conjecture for the Kasami monomials A concise proof of the 8 case of Sylvester's conjecture The Artin-Davenport conjecture on cubic forms The average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integer Perfect powers with few digits and $S$-unit coefficients Primitive Fourier Coefficients of Hermitian Klingen-Eisenstein Series Algebraic Eisenstein classes for $\mathrm{GL}_n$ with applications to the Bianchi case Generating and generalizing MSTD sets through Markov processes On S\'{a}rk\"{o}zy's Local Extrema Conjectures The least prime with a given primitive root and a variant of the larger sieve Local 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 permutations New algebraic points on covers of elliptic curves Mixing of the BCZ Map Higher additive energies on discrete cubes Block decompositions in the p-adic Langlands correspondence Semisimplicity, purity and Mumford-Tate conjecture for hyper-K\"ahler varieties Special Loci in the Moduli of Curves On the structure of certain valued fields II Random Cayley sum hypergraphs and $k$-fold sumsets

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 summand Gaps, isolated points, and the origin of the ray in the one-dimensional Dirichlet spectrum Exponential generating functions for Apostol-Dedekind and related sums Nonvanishing of special $L$-values of cusp forms on $\mathrm{GL}(2)$ with totally split prime power twists: without the class number hypothesis On Mahler $U$-numbers under rational maps Optimal large sieve for fixed order characters Moments and Large Geometric Monodromy for Linearly Constrained Kloosterman Families Sequential exponential-motivic periods in spatially cut-off $\phi^4_2$ Iterated cotangent-difference integrals over totally real cyclotomic fields Prescribed ideal classes and elliptic points in Ennola cubic fields Cubic Progressions on Smooth Plane Curves Note on fractional sum of the divisor function Few small primes suffice to cover unit groups Borwein-Bradley-type identities for Ramanujan-type series for $1/\pi^4$ Supercongruences for Domb numbers Proofs of some OEIS conjectures on Wythoff sums, Fibonacci and Lucas words Through the lens of the Eisenstein ideal Error Term Estimates for Sets of Remainders Dyadic 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 algebras On the generalized Sierpi\'nski and Riesel numbers One-level density of zeros of the Riemann zeta function weighted by its special values The main conjecture for a Vinogradov subsystem Sharp mean value estimates in the absence of translation-dilation invariance Four-square polynomial triples: quadratic classification and equal-degree obstructions On the factorization of $x^{d_{r}} + x^{d_{r-1}} + \cdots + x^{d_{2}} + x^{d_{1}} + p$ and a conjecture of C. Nicol Ab-faithfulness of absolute Galois groups in number theory Slope Stability for ${\mathbf Z}_p$-Towers of Curves Amicable numbers An Algebraic Proof of the Non-Modularity of Solutions to the Canonical Modular Differential Equation Ideal-Smooth Sets and an Explicit Upper Bound for the Real Sum-Product Exponent Automorphic commutator relations in relative geometric Langlands Conflict-avoiding codes and near-primitive roots A proper arithmetic surface with infinite \'etale fundamental group When the BSD Real Period Remembers Elliptic Curves over $\mathbb{Q}$ A Variant of the Fractional Gamma-regularized Zeta Kernel Tower of coverings and polylog-size coverings of rational points Theta Series with Half-integral Characteristics A Bogomolov property for moduli spaces of polynomials over abelian extensions How close can rational points get to a manifold? Counting zero-sum subspaces for the multiplicative inverse function Golod--Shafarevich for arithmetic surfaces Chowla Conjecture for the truncated M\"obius function over $\mathbb{F}_q[t]$ Degeneracy loci and unlikely intersections in abelian schemes $7$-adic Galois representations of elliptic curves over the rationals via Kummer descent The linear independence of $1$, $\zeta(3)$, and $\zeta(4)$ ETM-3D: A One-Parameter Multistable Quadratic Flow with an Explicit Absorbing Set and Intermittent Chaos Infinite log-concavity of the Taylor coefficients of the Riemann xi-function Uniform positivity of the tau invariant Weak approximation for Campana points on projective spaces Tempered Symplectic Distinction For Quaternionic $GL_n(D)$: A Conjecture of PRASAD On three conjectures of Kimberling concerning the array $\lfloor k\varphi^n\rfloor$ Polynomials with restricted support and maximal zeros on a finite Cartesian set Generic Hodge and special Hodge--Witt polygons Spreading out perverse sheaves

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 endomorphisms The proportion of polynomials over F_2 with positive orthogonal multiplicity Shimura Reciprocity for Real Quadratic Fields Counterexamples for Rational Points Near Curves The Prime Wavelet Tree: Compressing the Carmichael Numbers Extreme values of Dirichlet $L$-functions on the critical line with a growing prime modulus A uniform degree bound for modular rank-two Nahm sums The Wang--Sun Sum over Affine Derangements A new upper bound for the irrationality exponent of $\zeta(2)$ some arithmetical aspects of the two dimensional jacobian conjecture Telescopic Structure of Numerical Semigroups Generated by Unsigned Stirling Numbers of the First Kind Cohomology of Linearly Constrained Kloosterman Families: Newton Polytopes, Weights, and Boundary Monodromy Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves Split-Cubic Curves from D(n)-Triples: A Bounded Finite-Field Census Pellarin's Identity, Carlitz Period, and Anderson Generating Functions over Arbitrary Curves The quality plane of $abc$-triples and the decomposition into gains Gosper's and Ramanujan's infinite products and generalizations A cubic Chabauty criterion for hyperelliptic curves Eisenstein congruences in tame families and the class group of a metabelian extension Sum-product patterns in the shifted primes Hausdorff dimension for exactly approximable matrices Explicit second moments of symplectic Siegel transforms Quantitative Gowers uniformity of the primes in intervals of length $X^{5/8+\varepsilon}$ Exact diameter compression for four-point sumset cardinalities Pappas's conjecture on ramified unitary local models Resolving Erd\H{o}s-Ulam Monochromatic Union-Closed Family Conjectures Sharp rational points counting near nondegenerate curves in $\mathbb{R}^n$ Sturmian beta-shifts do not have typical periodic optimization

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 Characteristic PageRank on Lubotzky--Phillips--Sarnak graphs Some 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 rank New bounds for the integer Chebyshev constant of [0,1] On a problem on Ramanujan-Sato series of level 11 Perfect squares in reciprocal-sum sequences and primes that are inert in quadratic fields Congruence Jumping in Polynomial Divisibility Systems: Arithmetic Structure and Solution Sets Multiplicative recurrence of Piatetski--Shapiro and nil-Bohr sets Transcendence of dendric beta-expansions with pure discrete spectrum Powers in orbits and semigroups generated by polynomials Construction of parametrized families of general pseudo-bimagic and bimagic squares Baire-category transfer between Engel and Pierce expansions Indefinite theta vectors and generalized Nahm sums of arbitrary rank The sixth moment of the Riemann zeta function Translation invariant quadratic forms in $8$ variables and dense sets of primes Sharp $p$-adic Extrema and Least Extremal Rows for Restricted Binomial GCDs A Prime-Power Dichotomy for Nekrasov--Okounkov Hook Lengths and $t$-Core Partitions Tridimensional character sums with polynomial arguments and applications Uniform estimate of Lang-Weil type for counting points of schemes over finite rings Quadratic distances in even dimensions over prime fields Averages of Artin characters and their relation to the Davenport--Heilbronn theorem Square products of factorials and a conjecture of Erd\H{o}s and Graham Supersingularity and Superspeciality Verification of Abelian Surfaces Infinite free pro-p products as absolute Galois groups On the prime geodesic theorem On The Index of Polynomial Compositions over Valued Fields Direct Group Laws on Classical Genus-One Models Markov chains arising in the study of random matrices over pro-finite rings Transcending Algebraic Geometry Mock Modularity, Resurgence, and Dual False Theta Functions A Combinatorial Approach to the CUE Joint Moment Problem Intersecting integer partitions: star bounds and counterexamples at every scale Recurrent two-dimensional sequences over three and four letters simulating von Neumann constructions of finite ordinals Complex hyperbolic surfaces whose closed geodesics are all simple

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 powers Strong Artin Conjecture for Generalized Octahedral Representations in $\mathrm{GL}_3$ Large gaps between Romanoff numbers Euclidean Triangles Associated with Diophantine $D(4)$-triples Zeta elements for $p$-ordinary modular forms over imaginary quadratic fields and applications Monogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomials On a problem of Nathanson related to strongly minimal asymptotic bases of order $h$ The twisted convolution identity and ghost $r$-SICs from finite quantum dilogarithms The cardinality of a set containing the pairwise sums of four positive integers Limit distribution of algebraic integral points on curves Finite-slope p-adic L-functions for $\mathrm{GL}_{3}$ On the Quotient of a Pseudo-null Module Asymptotic and Arithmetic Aspects of Generalized Colored Overpartitions The sixth moment of a degree two $L$-function of arbitrary level Atkin--Lehner Quotients of Modular Curves at Primes of Bad Reduction Sharp spherical extension theorem in $\mathbb F_q^{2m}$ and applications On a question of Jones on tracelike vectors, cusp forms, and von Neumann algebras Rational quadrilaterals and tetrahedra -- the involutions of Kummer, Heegner and Regge Galois groups of random polynomials of large degree Semi-stable models, local heights and quadratic Chabauty for $X_0(N)^*$ A proof of Hirose's duality conjecture Resurgent rigidity of mock theta functions: uniqueness and natural boundary crossing On Greenberg's conjecture for rational elliptic curves at Eisenstein primes On c-polynomial factorisations The Bias Conjecture for One-Parameter, Non-Isotrivial Elliptic Curve Families On the coefficients of the asymptotic of analytic torsion Canonical representatives and interval independence in Ekedahl's equivalence Diameter and radius of an additive-multiplicative graph On Irreducibility and Multiplicity One Property for Non-Archimedean Type-II Theta Lifting

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-quotients Primes in arithmetic progressions and Siegel zeroes p-adic Rigidity and Supercongruences at Rank Two Attractors Strongly Pseudoperfect Numbers A $q$-analogue of a binomial supercongruence On closed-form expressions for weighted mean square of the Riemann zeta function and Dirichlet $L-$functions On Vojta's harder implication, height inequalities for admissible pairs, points of bounded degree and Deligne-Mumford stacks Twisted Diophantine Approximation I: Asymptotic Theory Twisted Diophantine Approximation II: Uniform Theory Reduction of Weil-Deligne Representations Farey Symbols for the Picard Group A Local Approach to Monogenity with an Application to Lenny Jones' Conjecture The Index of Composition of polynomials and its applications Collective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier Refinements On Boston's Unramified Conjecture for $\GL_2$ and McLeman's $(3,3)$-Conjecture The Algebra of Parity-Twisted Crank Moments and a Prime-Detecting Expression Truncated pretentious distances of multiplicative arithmetic functions On an infinite family of cubic fields with explicit fundamental units Products of two elements of Granville's random model in residue classes Multiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type Conjecture A closed-form law for the Salikhov-Zeilberger-Zudilin-Bai family, and computational evidence that Bai's point is optimal Weighted equidistribution of factorial prime valuations in fixed power bands An infinite family of counterexamples to Goss's conjecture on L-functions of cyclotomic function fields A negative answer to Erd\H{o}s Problem #786 Uniform Estimates for Integers with a Large Smooth Part A Short Proof of a Theorem of Pan and Zhang Ax-Schanuel for the Drinfeld $j$-function On minima of theta and Epstein zeta functions in dimension four Criterion set for diagonal forms of higher degree Restricted Binomial GCDs at Primes Congruent to -1 Smyth's Conjecture on the Mahler Measure of non-reciprocal trinomials of height $1$ Congruences for the Andrews--Uncu partition function $\mathcal{EO}_u(n)$ Computing residual representations of abelian threefolds with imaginary multiplication Improved exponent bounds for Erd\H{o}s--Selfridge curves Sharp Thresholds for Distance Patterns in Random Subsets of $\mathbb Z^d$ Resultants, Recursive Formulas and Binet Formulas for $\textrm{SU}(N)$ Verlinde Sums Square matrices with integer eigenvalues under entry permutations A Memory-Magic Exchange Law in Streaming Clifford+T Compilation Mordell--Lang plus Geometric Bogomolov

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 fields Efficient Computation and Congruences for Colored Partition Functions Quasimodular Forms, Partitions, and Primes in Intervals Conductors and Quadratic base change Factorizations in algebraic monogenic semidomains Unit fractions with semiprime denominators: an elementary proof of Erd\H{o}s Problem #306 On the sum of odd minimal excludants over overpartitions Matrix Solutions to the Diophantine equation $X^4+ Y^4=2Z^4$ On the Ordering and Injectivity of Lagrange Constants Associated with Certain Substitutions On Fermat-type equations of signature $(r,r,p)$ Congruences for Overcolored Partition $k$-tuples Restricted by Parity of the Parts Lower Bounds for Moments of Automorphic L-functions The infinite sum of the cubes of reciprocal balancing numbers Pseudo-Effectivity in the Skolem-Mahler-Lech Theorem Skew cyclic codes through Drinfeld modules Adelic reduction of module lattices A Unified Approach to Formal Arakawa-Kaneko Type Zeta Values via Iterated Integrals Escape and Non-Escape of Mass for Monogenic Binary Cubic Forms More than 83.69% of the zeros of the Riemann zeta function are distinct Dynamics of multiples of zeta by exponential functions Stacky Heights, Entropy, and Zeta Functions of Weighted Hypersurfaces over Finite Fields The Beilinson--Bloch heights of generalized Ceresa cycles Prime-Detecting Identities from Dirichlet Inversion On the distribution of the zeros of the Euler double zeta-function $\zeta_2(s,s)$ A Padovan-automatic description of a nested recurrence An elementary treatment of Ramanujan's elementary continued fractions Cancellation profiles of Fibonacci-Lucas zeta sums $k$-Fibonacci and $k$-Lucas numbers with the H\"older inequality Biases in the distribution of primes in short intervals Cyclotomic factors and irreducibility of the denominators of $q$-deformed rational numbers Necessary and sufficient condition for reciprocal polynomials to be monogenic The two-block odd partition function Rank stability of elliptic curves over $\mathbb{F}_q(t)$ in residue classes Higher-order colossally abundant numbers Omega bound for the Piltz divisor problem Square root cancellation in the hyperbolic lattice counting problem over cocompact groups An improved high-low method for the parabola Sums of von Mangoldt convolutions via trace-sum averages over $U(N)$ Coxeter Symmetry in Hypergeometric Functions and Elliptic Integral Moments Density of $\mu$-ordinary Primes for K3 Surfaces Exceptional poles of archimedean Asai $L$-functions Plectic Lie Algebra Action on Hilbert modular varieties Structure of derived Hecke algebras with coefficients in torsion-free profinite rings A new proof of two-color partition regularity of Pythagorean triples Hausdorff Dimension of Weighted Singular Vectors Moments of random multiplicative functions with polynomial coefficients Weak Hall's conjecture, approximation gains, and continued fractions Singular intersections in split semiabelian varieties On a generating function of the basis of weakly holomorphic functions on an elliptic curve Complete classification of $7$-adic Galois images for non-CM elliptic curves over $\Q$ A note on large clusters of $E_2$-numbers On the largest prime factors of $p-1$ and $p+1$ A difference formula of $p$-adic height pairings via the Bloch-Kato logarithm map Heavenly Elliptic Curves over Cubic Number Fields The modal expansion of Kempner sums Sharp lower bounds for the periodic maximal Schr\"odinger operator in higher dimensions Very sparse return sets in arithmetic dynamics A planar algebraic Zarankiewicz theorem over prime fields Generic Points on the Staircase and Irregularities in Uniform Distribution Uniform Unicellular Dessins d'Enfants with Trivial Automorphism Groups $p$-adic spectral zeta functions via the inverse Stieltjes transform A quasipolynomial inverse theorem for the $\mathsf{U}^k(\mathbb{F}_p^n)$ norm in the high characteristic Perfectoidness of Proper Shimura Varieties With Limpid Integral Models Gauss--Manin connections extend to holonomic coadmissible D-cap-modules Some applications of binary numeration systems with nonzero redundancy to the theory of locally complex functions Automorphic $C^*$-algebras of reductive groups A uniform lower bound for the Zhang-Kawazumi invariant and applications to the Bogomolov conjecture

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 Sums Supercharacter theory and applications to Ramanujan sums over a finite Frobenius ring On the Langlands--Kottwitz--Scholze method Congruence obstructions in the refined Koblitz conjecture Local Weak Maass Forms and Traces of Cycle Integrals Pinch's conjecture on $a$-convexity Mishiba's Conjecture on the Coaction of $\infty$-adic Multiple Zeta Values Counterexamples to the inhomogeneous Duffin-Schaeffer conjecture for a residual set of shifts Upper and lower fluctuations in Shallit's law of leap years in Pierce expansions Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture On the Moments of Least $r$-Gaps of Partitions and a Conjecture of Baruah and Talukdar The derivative function of the zeta-star correspondence Experiments on $3$-isogeny Selmer groups of elliptic curves with a $3$-torsion point A parametric Catalan-type congruence for generalized central trinomial coefficients Irreducible rootless unimodular lattices generated by vectors of norm $3$ Ternary Perfect Forms Over Imaginary Quadratic Field Further Results on Sum-Freedom of Binary and $q$-ary Functions On Conjectures of $\mu$-Invariant for Selmer Groups at $p=2$ Computing the Iwasawa $\mu$-Invariants for Elliptic Curves over $\mathbb{Z}_2$-Extensions On the infinite sum of reciprocals of the fourth powers of balancing numbers Free semigroups of power series Galois groups of integer polynomials with prescribed coefficients Formal groups and $(\varphi,\Gamma)$-modules Galois groups of twisted reciprocal polynomials: a uniform asymptotic The geometry of solutions to the general sextic Cartier--Dieudonn\'e Theory of Connected Group Schemes Comment on "Symmetric Pseudo-Random Matrices" A Mathematical Theory of Near-Field Super-Resolution

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 enumeration Effective logarithmic two-point Chowla bounds in every window Permutation binomials of the form $X^r(X^{q-1}+a)$ over finite fields Straight-line programs for the solutions of Pell's equation Computations of Cohomology of Arithmetic Groups, Part 1 On the index of generalized trinomials over Valued fields Computing the cohomology of Shimura curves in quasi-linear time Congruence Classes of Supporting the Erd\"{o}s-Straus Conjecture II: Wild Solutions A new lower bound for the Schur-Siegel-Smyth trace problem Refinements of Peck's theorem on simultaneous approximation to algebraic numbers Counting consecutive multiplicatively dependent triples A geometric proof of Peck's theorem A power-sum obstruction to cyclotomicity in a family of symmetric numerical semigroups Lie algebras for multiple Eisenstein series and multiple q-zeta values The Fermat-Type Matrix Equation over $\mathrm{GL}_2(\mathbb{Z})$ Reducibility of $rx^m+p^e f(x)$ for Large Primes $p$ On murmurations Arithmetic progressions in dense subsets of primitive elements of finite fields Self-intersection Points of Billiard Trajectories in a Square with Small Pockets On the density of $A+B$ when $B$ has few elements On smooth elements in arithmetic semigroups Infinitely Many Off-Critical-Line Zeros of the Tempered Xi Function: A Disproof of Yang's Conjecture Identities and congruences involving orthogonal polynomials and Ap\'ery-like numbers A note on isomorphism types of complete discretely valued fields of mixed characteristic Computing the divisor summatory function in $N^{9/28+o(1)}$ Sparsity of rational points on torsion level covers of Hilbert modular varieties Diophantine approximation by primes and Landau--Siegel zeros Lonely Runner Relations The Schur multiplier of $\rm{SL}_2$, $K_2$, and Dedekind zeta-functions over $S$-integers Pro-$\mathbf H_p$ density in the free group of rank two: a Frobenian criterion on the mod-$p$ torus Proof of the positive trace gap conjecture On the DML(1) property for regular endomorphisms of affine spaces: the $\mathbb{G}_m$-case Congruence Classes in $\mathbb{F}_p^2$: Sharp Results via an Energy Approach Disproof of a Conjectured Upper Bound for the Davenport Constant Total rings of quotients of higher dimensional Iwasawa algebras A computable wandering and tracelike vector for modular orbits in the Bergman space High Rank and Multiplicity in Random and Perfect Profinite Groups Frobenius lifts and point counting for smooth curves

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 proof Galois-Orbit Structure, Ramanujan Sums, and Stable-Range Collapse for Cyclotomic Cosine Formulas $A_2$-frames, negacyclic glue, and extremal strongly $6$-modular lattices The number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular variety Definability and undecidability via the torsion subgroup of units Completed cohomology of Hilbert modular varieties below middle degree Geometric lifting and Freiman's $3k-4$ theorem in compact connected abelian groups A proof of the Baruah--Gogoi conjecture on sums of odd and even overlined parts Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer Definite integral Albert algebras: arithmetic and finite geometry Modular integrals for individual modular knots Construction of vector-valued adelic automorphic forms Zero density estimates for $\mathrm{GL}_2$ automorphic $L$-functions Gevrey localization for simple and distinct zeros in a prime-modulus Dirichlet family An Approximate Version of Vu's Theorem on Economical Subbases For Non-Integer Exponents Shifted log-sine integrals and multiple zeta values Morse Topology, Zero Products, and Elliptic Prime Crossings On some $D(u^2)$-triples and quadruples of triangular numbers Beyond the unique pair: a two-parameter family of rational triangles with equal perimeter and area The Arithmetic of Reducible Rank 2 Hypergeometric Motives An Introduction to the Lagrange and Markov Spectra through the Lens of Generalized Markov Numbers Weighted bilinear identities and supercongruences for Ap\'ery-like polynomials On the hyperbolic prime number theorem Distinguishing Gauss sums A tyro's approach to the tilted sieve: beyond the Erd\H{o}s--Rankin bound Counting $k$-tuples of positive integers such that the values of several polynomials of $k$ variables are relatively prime Rankin-Cohen Pairings and Hilbert Hecke Eigenform Product Identities On the monomials of Poincar\'e Series of negative index Trivial zeros of zeta functions of type $\mathrm{A}_r$ Delta Characters and Filtered Isocrystals On the distribution of the minimal length of addition chains A Szemer\'edi-Trotter Theorem in Arbitrary Fields The intersection of local Arthur packets for even orthogonal groups and applications A minimal HRT counterexample at the sharp Gelfand--Shilov threshold Resultant of an equivariant polynomial system with respect to the reflection group $G(r,n)$ The Tate conjecture for powers of abelian fourfolds and the Hodge conjecture for powers of CM fourfolds Locally analytic representations in mixed characteristic via stacks Endoscopic liftings and parameters of epipelagic representations for classical groups Evaluating $\mathrm {SU}(3)$ Verlinde sums using spectral graph theory Computation of anisotropic singular sums from high-order derivatives of Epstein zeta functions

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 One Carmichael 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 study An Integral Representation of the Generalized Fibonacci Numbers Brauer-Kuroda relations for ramified graph covers The Sphere Packing Problem in Dimension 4 and the Twenty-Four-Cell Conjecture Moulds, Bimoulds, and some Lie algebras A density version for the sum of nine cubes of primes On the Euler transform and the floor function Distinct exponents in the prime factorization Irreducible polynomials with restricted digits in base $b(T)$ On the generation of multiplicative groups by small primes The density of sums of distinct divisors Density of large holes among power-free lattice points A surprising generalization of the M\"{o}bius function S-integrality for families of ordinary K3 surfaces and algebraicity theorems On the positivity of truncated pentagonal number series and some conjectures of Merca Irrationality Exponents and Partial Quotient Growth in Continued Fractions Abelian $p$-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 regular The weighted large sieve through Parseval Large values of the Hurwitz zeta function with rational parameter Equal subset sums and close divisors Boyd's conductor-11 Mahler measure conjecture: proof of the split-integral identity (C3), with an exact structural analysis of the family S_k A certified continuation machine for Mahler measure identities at CM points, with twelve new proofs of conjectures of Samart Peels of Equilateral Triangulated Surfaces On two families of period integrals related to Catalan's constant Improved rational approximations to Catalan's constant Cokernels of random $p$-adic orthogonal matrices and their linearizations Iterated integrals for generalized Appell functions A divisibility of automorphic periods for the real quadratic base change of $\mathrm{GL}_3$ Stable base change from unitary groups in three variables and integral relation of automorphic periods Remarks on the Geometry of Sets in $\mathbb{Z}^d$ with Small Fourier $L^1$ Norm The existence and uniqueness of magic-faced hypercubes, and applications to Khajuraho most-perfect magic squares, cubes, and hypercubes The Odlyzko-Poonen Conjecture on Irreducibility of Random Polynomials Extreme values of central $L$-derivatives and heights of Heegner points A finite arithmetic form of Robin's inequality and its equivalence to the Riemann hypothesis An irreducible decomposition of the Weil representation restricted to open compact subgroups The unique extremal threemodular lattice of rank 26, the generalized hexagon $(2,8)$, and the tight Cayley-plane $5$-design Approximating Pi (and other constants) by Radicals in the Footsteps of Rabbi Abraham Ibn Ezra and Guru RSJ Reddy Ergodic Averages over Shrinking Sectors of $\mathbb Z[i]$ Continuous Optimization for p-adic Models Zero-Run Spectra of the $(3,2)$ Raney numbers Modulo Primes Eisenstein scattering and Plancherel decomposition on cuspidal Bruhat-Tits quotients Resultant of an equivariant polynomial system with respect to a direct product of $r$ symmetric groups Support-Primitive Decomposition of Constacyclic Codes over Finite Fields: Coefficients-Based and Roots-Based Descriptions

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 Polynomials Iwasawa theory of class field towers A quadratic-residue dichotomy for two partition functions modulo 3 On periods of the Tribonacci sequence modulo primes Monogenic Fields of Cryptographic Size Bad Reduction of Genus Two Curves with complex multiplication Almost Trivial Units in Group Rings Zero density theorems for short intervals Maximal Unramified $p$-Extensions with Prescribed Galois Groups: A Quantitative Refinement of Ozaki's Theorem On a Tur\'an's theorem for small primes On a Tur\'an's theorem for arithmetic progressions Romanoff type theorems for polynomials over finite fields Steinness of the Basic $\mathrm{GL}_n$ Local Shimura Tower in Odd Rank On $\mathbb{Z}_2$-extensions of real quadratic fields with class group of $2$-rank three Counting number fields with symplectic Galois group The variance of the number of lattice points in narrow sectors Explicit bounds for the prime number theorem Wave Numbers: Discrete Sequence Algebras, Sieve Projectors, and Dynamical Geometry $v$-adic Chowla-Selberg formula over function fields Critical Pairs for Mixed Restricted Sumsets in Prime Fields A two-step supercongruence for an Ap\'ery-like sequence Large values of quadratic Hecke $L$-functions with prime-related moduli of the Gaussian field Lower-order terms in mean-square formulas for the Euler--Zagier double zeta-function and regularized multiple zeta values Higher Reciprocity, Cassels Pairings, and Selmer Towers for the 3/5 Congruent Number Problem Refined sum formulas for finite multiple zeta values of level two Two Legendre-symbol determinants of Sun and Bernoulli numbers Concave transforms and volumes of adelic line bundles Selmer groups of CM-twists of elliptic curves Interpolation determinants and the Lebesgue--Nagell equation $a^2-D=b^p$ On the noninjectivity of Jordan's totient functions Detecting split surfaces, RM surfaces, and minimum walks on isogeny graphs Non-Archimedean Poincar\'e series and geodesics on the Bruhat-Tits tree The exceptional set of a prime and a square On existence of generalised Lehmer numbers modulo primes Imaginary Non-CM Fields of $2$-Power Degree A fully faithful p-adic Riemann--Hilbert functor for filtered coherent D-modules Proofs of eighteen conjectural identities related to the modulo nine Kanade--Russell identities Sharp zero estimates for trajectories of polynomial vector fields Proportions of the non-trivial zeros of the Riemann zeta function Selberg sieve weights and sign changes of Kloosterman sums. I. Uniform asymptotics for shifted weights Selberg sieve weights and sign changes of Kloosterman sums. II. Square-free moduli with at most four prime factors On the abundance of rigid meromorphic cocycles for quadratic forms in four variables The lower bound of shifted primes with large prime factors $D$-elliptic modular curves $X_0(N)$ Asymptotic Behavior of Iterated Sets of Remainders Weighted Generalizations of Zagier's Phenomenon The local Dold congruence for Fibonacci and Lucas sequences On Normality Preserving Operations Geometry around unramified CM points Algebraic independence of periods of Anderson modules and their hyperderivatives Exceptional maps and abelian points in backward orbits A polynomial basis for the multizeta algebra in positive characteristic Abelian dynamical Galois groups over global function fields $\Kab$ has the Bogomolov property for canonical heights The Hall-Janko Simple Group and the Icosian Leech Lattice Extremal Least Common Multiples in Rows of Pascal's Triangle Existence of a Hall ray in higher dimensional Lagrange spectra Sum of Three Squares and Particle in a Cubic Box - Degeneracies Quantum modularity in refined topological recursion Fundamental Lemmas in Universal Resolution From Dimension Drop to Aperiodic Order Density of almost squares of horospherical orbits in non-uniform quotients of $\operatorname{SL}_2(\mathbb{R})\times\operatorname{SL}_2(\mathbb{R})$

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 lattices Extreme value laws for intrinsic Diophantine approximation on spheres Eigenvectors of $p$-Curvature for Geometric Difference Equations Galois deformation rings and modularity in the residually reducible case On The Cyclicity of Algebraic Lattices The large sieve for square moduli under Hooley's hypothesis $R^*$ Annular Frobenius Classification of p-adic Stieltjes--Schwarzian Equations The integer group determinants for $\mathbb{Z}_p^n$ Difference of the Sum of All Odd and Even Overlined Parts of Overpartitions Frobenius Numbers Associated with Primitive Pythagorean Quadruples Arithmetic structure of $L_2$-norms of ${\mathrm{SL}}_2(\mathbb{Z})$ matrices A Note On Certain Minimal Excludants Over Overpartitions On low-discrepancy sequences and Poissonian pair correlation Higher Labute-Serre duality and Lyndon words Non-existence of sets with few special directions Real quadratic fields and finite quantum dilogarithms I $\mathbf{Bad}(\mathbf{r};\mathbf{s})$ is Hyperplane Absolute Winning An equivariant version of Gabber's lemma On the Injectivity of Elementary Symmetric Partitions and the Multiset Recovery Problem

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