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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 sublatticesDiscrete dynamics of Eratosthenes sieve$k$-Lucas Annulus for Polynomial ZerosA Neighbouring-Denominator Case of the Erd\H{o}s--Mahler ConjecturePeriod Relations for Theta Products and Elliptic Integral MomentsThe 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 characteristicTorsion-vanishing for Siegel modular varieties v
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 intervalsTranscendence of Tonelli--Shanks Power Modulo Infinitely Large PrimesJacob's ladders, new classes of sum variants of almost linear formula and corresponding $\zeta$-functionals and $\zeta$-equivalents of the Fermat-Wiles theoremThe equality cases $P_t(\mathbb{N})=\tfrac12$ for the deconvolved sum-of-digits measuresThe uniform Littlewood conjecture fails on a set of positive Hausdorff dimensionThe divisor function for matricesPseudonullity f
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 familiesFourier Spectral Reciprocity and Canonical Hecke $L$-FunctionsGeometric Realization of Finite Residue Casimirs and Weil Operators via Szeg\H{o} KernelsSieve 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 IntegralsWinning property of counterexamples to Unifo
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 conjectureRational Points and Brownian MotionDense ascending waves: A resolution of the Alon-Spencer conjectureHow 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 ConjecturesGeneral Stirling-Ramanujan Constants are exponential periods and applicationsPrime multipliers of order ten: norm spectra, local charts, and select
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 rootsPolylogarithmic Chabauty--Kim loci over number fieldsMaximal and minimal curves of the form $y^3=x^{(q^2+1)/2}+x$Euler characteristic of the Selmer group attached to an Artin representationComplete Resolution Of A Family Of Twisted Thue EquationsArithmetic $\mathcal{D}$-modules over Laurent series fields: the relative caseAdjoint Closures of Singular Pairs of Quadratic Forms and a Pfister-Type CriterionLegendre polynomials and complex multiplication, II: class
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 indexAn Algebraic Approach to the Fundamental Theorem of AlgebraMany Representations as Sums of Three Prime Cubes${}_5F_4$ evaluations and a family of $\pi^2+\log^2$ identitiesOn the Finiteness of Isolated $j$-invariants for $X_1(N)$Quantitative bounds for sets lacking polynomial progressions with shifted prime differenceArithmetic partial differential operators on ramified extensions of $\ZZ_p$Forced Shadows of an Obstructed Hyperbolic K
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/2026-08-20/ On sums of two primes and six Fibonacci numbersProperties of Kloosterman sums for long Weyl element on GL(n)Rational Solids with Equal Surface Area and VolumeSharp Transitions for Localized Solutions to a Diophantine InequalityMean Value Estimates for a Real-Exponent Analogue of Waring's ProblemAsymptotics of Hecke polynomial coefficients on the Atkin-Lehner eigenspacesOn $p$-adic solubility of $Ax^\ell + By^m + Cz^n = 0$Hecke-type action on higher order Herglotz-Zagier functionOn the Diopha
arXiv math.NTの新着論文18本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-19/ Prime-Exponent Transition Geometry and Divisor Barriers Between Consecutive Highly Composite NumbersAlgebraic Lattices Arising from Congruence Submodules in Subfields of $p$-th Cyclotomic FieldsMild p-Class Tower Groups of Imaginary Quadratic FieldsOn Buzzard's TheorenShifted second moment of Gaussian Hecke $L$-functions $L(s,\lambda^k)$A central limit theorem for prime geodesics on random surfaces of large genusRibet bimodules and principally polarized superspecial abelian varieties with qu
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/2026-08-18/ A descent-set obstruction for the Casas-Alvero conjectureExponential sums over primesReciprocity for The Short Twisted Second Moment of The Riemann Zeta FunctionBounding The Number of Zeros Near the Central Point in Families of Cuspidal NewformsTranscendence of continued fractions over function fields and a quantitative version of Uchiyama's theoremAlgebraic geometric framework of Rogers--Ramanujan identitiesInterlacing for zeros of the Serre derivative of Eisenstein seriesPositive quasimodu
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/2026-08-17/ On the Existence of Hyperelliptic Curves over $\mathbb{Q}(T)$ with Certain Jacobian RanksMore than two thirds of the zeta zeros are simple and on the critical lineSome Dwork-type $q$-supercongruences from a $_6\phi_5$ summation formula$p$-numerical semigroup of the sequence of consecutive odd integersA structural trace identity and certified spectra for the Richelot-Brandt graphA Kubilius model for sieve-theoretic sequencesRatio of sum of digits functions in two basesHurwitz class number rel
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/2026-08-14/ On Waring--Goldbach problem with mixed powersGeneralized Addition Theorems for the Jacobi Elliptic FunctionsA conditional arithmetic obstruction to the prime numbers as a spectrum of a probability measureFinding all cospectral mates over a number fieldSpecial Values of Shifted Dirichlet Series from an Adjoint Map on Almost Holomorphic Modular FormsDensity bounds for permutations avoiding monotone arithmetic progressionsEscalations and criteria over real quadratic fieldsAlgebraic construction
arXiv math.NTの新着論文18本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-13/ The motivic Selmer scheme of the thrice-punctured lineUpper bound for the moment of shifted values of cubic $L$-functions over function fieldsGalois Symbols for a Jacobian and Multiplicative GroupsEqualities among simplest quartic fields: a complete classificationHeight lower bounds for elements of highly composite ringsA $p$-part Birch and Swinnerton-Dyer Formula over Totally Imaginary Quadratic Extension of Totally Real FieldsHasse-Witt invariants for trace forms of Jacobi polynomialsDuali
arXiv math.NTの新着論文16本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-12/ On the Squarefree Values of Degree-$2q$ PolynomialsAn omega result for the first sign change of coefficients of symmetric power $L$-functions of Hecke-Maass cusp formsA proof of a weighted sum conjecture for finite multiple zeta values of level twoAverage root numbers in two isotrivial families of elliptic curvesPermutation polynomials from the trace functionsBockstein Spectral Sequences and Applications to the Tame Fontaine Mazur ConjectureDistinguishing elliptic curves modulo $p$ and ident
arXiv math.NTの新着論文37本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-11/ Zeta zeros of function fields heuristically equidistribute as genus goes to infinitySharp vertex connectivity of the Markoff graphs modulo $p$Positive Lower Density for Hofstadter's $ab-1$ ProblemOn the Emerton-Gee stack of potentially semistable representationsRepresentations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's ConjecturesWhich numbers are $u$-invariants of perfectoid fields?Binomial coefficients coprime to 6Short Second Moment of $\mathrm{GL}(2)$ L-Functions
arXiv math.NTの新着論文15本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-10/ Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor CoversSquarefree numbers in short intervals: explicit and formalizedAnticyclotomic Iwasawa theory of CM elliptic curves at ramified primesA Combinatorial Approach to Vorono{\"i} TheoryAn extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for $\zeta_\mathbb{F}(2)$ and $\zeta_\mathbb{F}(2m+1)$On semi-stable integral models for Shimura varietiesModularity of Higher Theta Series III: P
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/2026-08-07/ Rigidity of Averages over the Two Largest Prime FactorsExplicit Algebraic Numbers all whose Integer Parts of Powers are CompositeThe sesquicentennial of the prime number $2^{127} - 1$Trianguline representations and locally analytic principal series of ${\rm GL}_2({\mathbb Q}_p)$Asymptotic uncorrelations between functions with squarefull kernel and functions of invariant averageModularity of Point Counts for the Curves $X^a=Y^b$: New Rogers--Ramanujan IdentitiesIwasawa invariants and exceptio
arXiv math.NTの新着論文16本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-06/ Rational spanning sets of level-one cusp forms from Eisenstein series at prime levelsThe distribution and the structure of the maximum of partial sums in families of trace functionsThe $5$-divisible integer group determinants for the elementary abelian group of order 25On the Burgess bound and Pythagorean triples involving primitive rootsPowers as Fibonacci SumsRegularized Multitangent Functions and Reduction TheoremConstruction Of Non-Odd Galois Representations With Large ImageOn the $L^2$
arXiv math.NTの新着論文16本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-05/ A Classification of Multiply Monogenic Quartic OrdersCounting in Vieta graphs over $\mathbb{F}_p$On pairs of primes with small order reciprocityAdmissible Pairs: A Variation to Pollock ConjecturesMellin Transform Formulas for Anderson Modules and Hints of ModularityErd\H{o}s-Moser Equation in Arithmetic ProgressionsExplicit Jordan decompositions for ideal lattices in CM fieldsNo three algebraic conjugates of degree sixteen sum to zeroAn upper bound for counting algebraic tori over $\mathbb{Q
arXiv math.NTの新着論文54本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-04/ Random Multiplicative Functions with Periodic WeightsLjunggren--Jacobsthal and Bailey-Type Congruences for Rectangular Gaussian Binomial CoefficientsAsymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fieldsPositive rational series for reciprocal powers of Catalan's constant and Dirichlet beta valuesNegative bias in moments of the Legendre family of elliptic curvesMachine learning the arithmetic of Boyd's Mahler measure conjecturesFaster Deterministic In
arXiv math.NTの新着論文10本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-03/ Multiplicative dependence in the sumset of multiplicative groupsThe Fine-Structure Hierarchy of Prime Biases and the Universal Dominance of $-1 \pmod N$Small points in radical extensions of number fieldsGeneralized Wieferich primes and monogenic trinomialsAn Introduction to p-adic Hodge TheoryA sharp almost sure upper bound for partial sums of random multiplicative functionsOn the size of $h$-fold sumsetsThe least quadratic residue and integers represented by quadratic formsOn Generalized Ch
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/2026-07-31/ The exceptional set of the Goldbach problemMultivariate counting of wild abelian extensionsOn some Diophantine and Ergodic properties of the Schneider map over function fieldsOn the greatest common divisor of $n, \lfloor \alpha_1n\rfloor, \lfloor \alpha_2n^2\rfloor, ..., \lfloor \alpha_kn^k\rfloor$An Asymptotic Bound for Non-covering Congruence Systems over Fq[x]Perfect $2$-codes over arbitrary alphabetsSchur Eisenstein series and Schur MacMahon seriesIrrationality of finite logarithms in a
arXiv math.NTの新着論文18本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-30/ On purity of Anderson t-modulesInclusions between p-bounded crystalline loci in dimension twoBhargava Gamma functions for determinant-admissible setsOn the transcendence of twisted special $L$-values at non-negative integers in characteristic $p$Improved Bounds for Distinct Multiples in IntervalsOn Oliver's relations between infinite series and infinite productsOn a Question of Lehmer concerning the Comtet NumbersOn the higher algebraic $K$-groups of arithmetically equivalent number fieldsEx
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/2026-07-29/ Extremal Chowla sets and their linear analogues: A human-AI mathematical investigation using Co-ScientistTranscendence of multivariate Mahler functions and algebraic relations between their valuesTwisted automorphic descent to odd GSpin groups and applicationsOn certain $D(9)$ and $D(64)$ Diophantine triplesThe Explicit Hypergeometric Modularity Method IIIDiagonal cycles on Shtukas and the adjoint $L$-functionOn the Vanishing of the Brauer-Manin Obstruction for Normic BundlesBeyond endoscopy
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/2026-07-28/ Jittered sampling and probability measuresTadpole Nahm sum as a WronskianUnshared zeros of Dirichlet $L$-functionsOn the Frobenius Number of Quotients of Numerical SemigroupsFinite length for unramified $\mathrm{GL}_2$: beyond multiplicity one, non-semisimple caseOn the role of higher roots in prime ideal racesExplicit Twisted Hilbert Class Components Beyond Classical IrregularityOn the Comparison of the D-new Modular Degree and the Shimura Degree of Modular Abelian VarietiesModularity of Na
arXiv math.NTの新着論文11本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-27/ Explicit bounds for Buchstab's functionA More Efficient Algorithm for Finding the Number of Permutations of $\mathbb{ZZ}/n\mathbb{ZZ}$ with Distinct Partial SumsFactorial Calculi and the Canonical Stirling Defect of the Prime Bhargava FactorialDensities of arithmetic Hecke triangle group orbitsExplicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\mathfrak f$Prime-Interval AlgebrasCongruences for the coefficients of MacMah
