構造と数論と幾何学の探求 - 2026/10/27の論文53本

arXiv math.NTの新着論文53本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-27/ A Sharp Distributional Lower Bound for Planar Discrepancy On the unit group of some triquadratic fields Two parametric $q$-supercongruences from Andrews' multi-series transformation On the evenness of coefficients of modular forms A secondary term in the first moment of cubic $L$-functions over function fields Local obstructions and certified computations for perfect powers in power sums Height growth of rational self-maps Squarefree Values of Random Polynomials On Lehmer's Problem Zassenhaus Filtration and Ihara Constants Joint Extension Field Point Counts for Superelliptic Curves Exploring topological features of a complex network of prime factors and composite numbers Explicit Coleman integration over finite extensions of $\mathbb{Q}_p$ Finite-sum Identities and Supercongruences for Cubes of Catalan Numbers Cross numbers and the characterization of finite abelian groups by length sets Three Quadratic Recurrences Modulo 3: What We Can Prove and What We Can Guess On real biquadratic number fields for which the $2$-Iwasawa module has rank $3$ A symmetric extension of Zhao's series for $\zeta(5)$ Frangible prime gaps Results for distinct covering systems with a prime minimum modulus $q \ge 11$ Admissible sets of integers in imaginary quadratic fields of class number 1 Finiteness theorems for trace Euclidean quadratic lattices over totally real number fields Geometric progressions in distance sets in odd dimensions over prime fields The Family $X_{qp^s}$ for Distinct Primes $q,p$ in Connection with Carmichael's Totient Conjecture Hartl's dictionary and a transcendence characterization of equicharacteristic local shtukas with complex multiplication Dynamical Chowla conjecture for polynomials of several variables Counting Integral Matrices with Given Cubic Characteristic Polynomial Non-liftability of the field of norms of the $p$-adic false Tate curve extension On almost perfect additive complements Galois groups of polynomials over a fixed number field: determinant methods in general boxes, resolvents, and quantitative counting Weighted density bounds for covering sy