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 DiscrepancyOn the unit group of some triquadratic fieldsTwo parametric $q$-supercongruences from Andrews' multi-series transformationOn the evenness of coefficients of modular formsA secondary term in the first moment of cubic $L$-functions over function fieldsLocal obstructions and certified computations for perfect powers in power sumsHeight growth of rational self-mapsSquarefree Values of Random PolynomialsOn Lehmer's ProblemZassenhaus Filtration and Ihara ConstantsJoint Extension Field Point Counts for Superelliptic CurvesExploring topological features of a complex network of prime factors and composite numbersExplicit Coleman integration over finite extensions of $\mathbb{Q}_p$Finite-sum Identities and Supercongruences for Cubes of Catalan NumbersCross numbers and the characterization of finite abelian groups by length setsThree Quadratic Recurrences Modulo 3: What We Can Prove and What We Can GuessOn 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 gapsResults for distinct covering systems with a prime minimum modulus $q \ge 11$Admissible sets of integers in imaginary quadratic fields of class number 1Finiteness theorems for trace Euclidean quadratic lattices over totally real number fieldsGeometric progressions in distance sets in odd dimensions over prime fieldsThe Family $X_{qp^s}$ for Distinct Primes $q,p$ in Connection with Carmichael's Totient ConjectureHartl's dictionary and a transcendence characterization of equicharacteristic local shtukas with complex multiplicationDynamical Chowla conjecture for polynomials of several variablesCounting Integral Matrices with Given Cubic Characteristic PolynomialNon-liftability of the field of norms of the $p$-adic false Tate curve extensionOn almost perfect additive complementsGalois groups of polynomials over a fixed number field: determinant methods in general boxes, resolvents, and quantitative countingWeighted density bounds for covering systems over Dedekind domainsBounds on the number of squares in recurrence sequences: $y_{0}=b^{2}$ (II)Congruences modulo powers of $7$ for partitions with colored odd partsSpectral zeta functions in positive characteristicOn Hecke algebras at exceptional Eisenstein primesOn the Hasse principle for a block-diagonal form and a form of lower degreeOn explicit formulas for Grassmannian polylogarithms and Gelfand-MacPherson formsImproved lattice-packing bounds in small dimensionsOn the magic positivity of the Ehrhart polynomials of dilated base polyto