幾何学的対象と数論的解析 - 2026/10/8の論文29本

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