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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 CharacteristicPageRank on Lubotzky--Phillips--Sarnak graphsSome 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 rankNew bounds for the integer Chebyshev constant of [0,1]On a problem on Ramanujan-Sato series of level 11Perfect squares in reciprocal-sum sequences and primes that are inert in quadratic fieldsCongruence Jumping in Polynomial Divisibility Systems: Arithmetic Structure and Solution SetsMultiplicative recurrence of Piatetski--Shapiro and nil-Bohr setsTranscendence of dendric beta-expansions with pure discrete spectrumPowers in orbits and semigroups generated by polynomialsConstruction of parametrized families of general pseudo-bimagic and bimagic squaresBaire-category transfer between Engel and Pierce expansionsIndefinite theta vectors and generalized Nahm sums of arbitrary rankThe sixth moment of the Riemann zeta functionTranslation invariant quadratic forms in $8$ variables and dense sets of primesSharp $p$-adic Extrema and Least Extremal Rows for Restricted Binomial GCDsA Prime-Power Dichotomy for Nekrasov--Okounkov Hook Lengths and $t$-Core PartitionsTridimensional character sums with polynomial arguments and applicationsUniform estimate of Lang-Weil type for counting points of schemes over finite ringsQuadratic distances in even dimensions over prime fieldsAverages of Artin characters and their relation to the Davenport--Heilbronn theoremSquare products of factorials and a conjecture of Erd\H{o}s and GrahamSupersingularity and Superspeciality Verification of Abelian SurfacesInfinite free pro-p products as absolute Galois groupsOn the prime geodesic theoremOn The Index of Polynomial Compositions over Valued FieldsDirect Group Laws on Classical Genus-One ModelsMarkov chains arising in the study of random matrices over pro-finite ringsTranscending Algebraic GeometryMock Modularity, Resurgence, and Dual False Theta FunctionsA Combinatorial Approach to the CUE Joint Moment ProblemIntersecting integer partitions: star bounds and counterexamples at every scaleRecurrent two-dimensional sequences over three and four letters simulating von Neumann constructions of finite ordinalsComplex 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 powersStrong Artin Conjecture for Generalized Octahedral Representations in $\mathrm{GL}_3$Large gaps between Romanoff numbersEuclidean Triangles Associated with Diophantine $D(4)$-triplesZeta elements for $p$-ordinary modular forms over imaginary quadratic fields and applicationsMonogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomialsOn a problem of Nathanson related to strongly minimal asymptotic bases of order $h$The twisted convolution identity and ghost $r$-SICs from finite quantum dilogarithmsThe cardinality of a set containing the pairwise sums of four positive integersLimit distribution of algebraic integral points on curvesFinite-slope p-adic L-functions for $\mathrm{GL}_{3}$On the Quotient of a Pseudo-null ModuleAsymptotic and Arithmetic Aspects of Generalized Colored OverpartitionsThe sixth moment of a degree two $L$-function of arbitrary levelAtkin--Lehner Quotients of Modular Curves at Primes of Bad ReductionSharp spherical extension theorem in $\mathbb F_q^{2m}$ and applicationsOn a question of Jones on tracelike vectors, cusp forms, and von Neumann algebrasRational quadrilaterals and tetrahedra -- the involutions of Kummer, Heegner and ReggeGalois groups of random polynomials of large degreeSemi-stable models, local heights and quadratic Chabauty for $X_0(N)^*$A proof of Hirose's duality conjectureResurgent rigidity of mock theta functions: uniqueness and natural boundary crossingOn Greenberg's conjecture for rational elliptic curves at Eisenstein primesOn c-polynomial factorisationsThe Bias Conjecture for One-Parameter, Non-Isotrivial Elliptic Curve FamiliesOn the coefficients of the asymptotic of analytic torsionCanonical representatives and interval independence in Ekedahl's equivalenceDiameter and radius of an additive-multiplicative graphOn 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-quotientsPrimes in arithmetic progressions and Siegel zeroesp-adic Rigidity and Supercongruences at Rank Two AttractorsStrongly Pseudoperfect NumbersA $q$-analogue of a binomial supercongruenceOn closed-form expressions for weighted mean square of the Riemann zeta function and Dirichlet $L-$functionsOn Vojta's harder implication, height inequalities for admissible pairs, points of bounded degree and Deligne-Mumford stacksTwisted Diophantine Approximation I: Asymptotic TheoryTwisted Diophantine Approximation II: Uniform TheoryReduction of Weil-Deligne RepresentationsFarey Symbols for the Picard GroupA Local Approach to Monogenity with an Application to Lenny Jones' ConjectureThe Index of Composition of polynomials and its applicationsCollective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier RefinementsOn Boston's Unramified Conjecture for $\GL_2$ and McLeman's $(3,3)$-ConjectureThe Algebra of Parity-Twisted Crank Moments and a Prime-Detecting ExpressionTruncated pretentious distances of multiplicative arithmetic functionsOn an infinite family of cubic fields with explicit fundamental unitsProducts of two elements of Granville's random model in residue classesMultiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type ConjectureA closed-form law for the Salikhov-Zeilberger-Zudilin-Bai family, and computational evidence that Bai's point is optimalWeighted equidistribution of factorial prime valuations in fixed power bandsAn infinite family of counterexamples to Goss's conjecture on L-functions of cyclotomic function fieldsA negative answer to Erd\H{o}s Problem #786Uniform Estimates for Integers with a Large Smooth PartA Short Proof of a Theorem of Pan and ZhangAx-Schanuel for the Drinfeld $j$-functionOn minima of theta and Epstein zeta functions in dimension fourCriterion set for diagonal forms of higher degreeRestricted Binomial GCDs at Primes Congruent to -1Smyth'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 multiplicationImproved exponent bounds for Erd\H{o}s--Selfridge curvesSharp Thresholds for Distance Patterns in Random Subsets of $\mathbb Z^d$Resultants, Recursive Formulas and Binet Formulas for $\textrm{SU}(N)$ Verlinde SumsSquare matrices with integer eigenvalues under entry permutationsA Memory-Magic Exchange Law in Streaming Clifford+T CompilationMordell--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 fieldsEfficient Computation and Congruences for Colored Partition FunctionsQuasimodular Forms, Partitions, and Primes in IntervalsConductors and Quadratic base changeFactorizations in algebraic monogenic semidomainsUnit fractions with semiprime denominators: an elementary proof of Erd\H{o}s Problem #306On the sum of odd minimal excludants over overpartitionsMatrix Solutions to the Diophantine equation $X^4+ Y^4=2Z^4$On the Ordering and Injectivity of Lagrange Constants Associated with Certain SubstitutionsOn Fermat-type equations of signature $(r,r,p)$Congruences for Overcolored Partition $k$-tuples Restricted by Parity of the PartsLower Bounds for Moments of Automorphic L-functionsThe infinite sum of the cubes of reciprocal balancing numbersPseudo-Effectivity in the Skolem-Mahler-Lech TheoremSkew cyclic codes through Drinfeld modulesAdelic reduction of module latticesA Unified Approach to Formal Arakawa-Kaneko Type Zeta Values via Iterated IntegralsEscape and Non-Escape of Mass for Monogenic Binary Cubic FormsMore than 83.69% of the zeros of the Riemann zeta function are distinctDynamics of multiples of zeta by exponential functionsStacky Heights, Entropy, and Zeta Functions of Weighted Hypersurfaces over Finite FieldsThe Beilinson--Bloch heights of generalized Ceresa cyclesPrime-Detecting Identities from Dirichlet InversionOn the distribution of the zeros of the Euler double zeta-function $\zeta_2(s,s)$A Padovan-automatic description of a nested recurrenceAn elementary treatment of Ramanujan's elementary continued fractionsCancellation profiles of Fibonacci-Lucas zeta sums$k$-Fibonacci and $k$-Lucas numbers with the H\"older inequalityBiases in the distribution of primes in short intervalsCyclotomic factors and irreducibility of the denominators of $q$-deformed rational numbersNecessary and sufficient condition for reciprocal polynomials to be monogenicThe two-block odd partition functionRank stability of elliptic curves over $\mathbb{F}_q(t)$ in residue classesHigher-order colossally abundant numbersOmega bound for the Piltz divisor problemSquare root cancellation in the hyperbolic lattice counting problem over cocompact groupsAn improved high-low method for the parabolaSums of von Mangoldt convolutions via trace-sum averages over $U(N)$Coxeter Symmetry in Hypergeometric Functions and Elliptic Integral MomentsDensity of $\mu$-ordinary Primes for K3 SurfacesExceptional poles of archimedean Asai $L$-functionsPlectic Lie Algebra Action on Hilbert modular varietiesStructure of derived Hecke algebras with coefficients in torsion-free profinite ringsA new proof of two-color partition regularity of Pythagorean triplesHausdorff Dimension of Weighted Singular VectorsMoments of random multiplicative functions with polynomial coefficientsWeak Hall's conjecture, approximation gains, and continued fractionsSingular intersections in split semiabelian varietiesOn a generating function of the basis of weakly holomorphic functions on an elliptic curveComplete classification of $7$-adic Galois images for non-CM elliptic curves over $\Q$A note on large clusters of $E_2$-numbersOn the largest prime factors of $p-1$ and $p+1$A difference formula of $p$-adic height pairings via the Bloch-Kato logarithm mapHeavenly Elliptic Curves over Cubic Number FieldsThe modal expansion of Kempner sumsSharp lower bounds for the periodic maximal Schr\"odinger operator in higher dimensionsVery sparse return sets in arithmetic dynamicsA planar algebraic Zarankiewicz theorem over prime fieldsGeneric Points on the Staircase and Irregularities in Uniform DistributionUniform Unicellular Dessins d'Enfants with Trivial Automorphism Groups$p$-adic spectral zeta functions via the inverse Stieltjes transformA quasipolynomial inverse theorem for the $\mathsf{U}^k(\mathbb{F}_p^n)$ norm in the high characteristicPerfectoidness of Proper Shimura Varieties With Limpid Integral ModelsGauss--Manin connections extend to holonomic coadmissible D-cap-modulesSome applications of binary numeration systems with nonzero redundancy to the theory of locally complex functionsAutomorphic $C^*$-algebras of reductive groupsA 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 SumsSupercharacter theory and applications to Ramanujan sums over a finite Frobenius ringOn the Langlands--Kottwitz--Scholze methodCongruence obstructions in the refined Koblitz conjectureLocal Weak Maass Forms and Traces of Cycle IntegralsPinch's conjecture on $a$-convexityMishiba's Conjecture on the Coaction of $\infty$-adic Multiple Zeta ValuesCounterexamples to the inhomogeneous Duffin-Schaeffer conjecture for a residual set of shiftsUpper and lower fluctuations in Shallit's law of leap years in Pierce expansionsCounterexamples to the inhomogeneous Duffin-Schaeffer ConjectureOn the Moments of Least $r$-Gaps of Partitions and a Conjecture of Baruah and TalukdarThe derivative function of the zeta-star correspondenceExperiments on $3$-isogeny Selmer groups of elliptic curves with a $3$-torsion pointA parametric Catalan-type congruence for generalized central trinomial coefficientsIrreducible rootless unimodular lattices generated by vectors of norm $3$Ternary Perfect Forms Over Imaginary Quadratic FieldFurther Results on Sum-Freedom of Binary and $q$-ary FunctionsOn Conjectures of $\mu$-Invariant for Selmer Groups at $p=2$Computing the Iwasawa $\mu$-Invariants for Elliptic Curves over $\mathbb{Z}_2$-ExtensionsOn the infinite sum of reciprocals of the fourth powers of balancing numbersFree semigroups of power seriesGalois groups of integer polynomials with prescribed coefficientsFormal groups and $(\varphi,\Gamma)$-modulesGalois groups of twisted reciprocal polynomials: a uniform asymptoticThe geometry of solutions to the general sexticCartier--Dieudonn\'e Theory of Connected Group SchemesComment 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 enumerationEffective logarithmic two-point Chowla bounds in every windowPermutation binomials of the form $X^r(X^{q-1}+a)$ over finite fieldsStraight-line programs for the solutions of Pell's equationComputations of Cohomology of Arithmetic Groups, Part 1On the index of generalized trinomials over Valued fieldsComputing the cohomology of Shimura curves in quasi-linear timeCongruence Classes of Supporting the Erd\"{o}s-Straus Conjecture II: Wild SolutionsA new lower bound for the Schur-Siegel-Smyth trace problemRefinements of Peck's theorem on simultaneous approximation to algebraic numbersCounting consecutive multiplicatively dependent triplesA geometric proof of Peck's theoremA power-sum obstruction to cyclotomicity in a family of symmetric numerical semigroupsLie algebras for multiple Eisenstein series and multiple q-zeta valuesThe Fermat-Type Matrix Equation over $\mathrm{GL}_2(\mathbb{Z})$Reducibility of $rx^m+p^e f(x)$ for Large Primes $p$On murmurationsArithmetic progressions in dense subsets of primitive elements of finite fieldsSelf-intersection Points of Billiard Trajectories in a Square with Small PocketsOn the density of $A+B$ when $B$ has few elementsOn smooth elements in arithmetic semigroupsInfinitely Many Off-Critical-Line Zeros of the Tempered Xi Function: A Disproof of Yang's ConjectureIdentities and congruences involving orthogonal polynomials and Ap\'ery-like numbersA note on isomorphism types of complete discretely valued fields of mixed characteristicComputing the divisor summatory function in $N^{9/28+o(1)}$Sparsity of rational points on torsion level covers of Hilbert modular varietiesDiophantine approximation by primes and Landau--Siegel zerosLonely Runner RelationsThe Schur multiplier of $\rm{SL}_2$, $K_2$, and Dedekind zeta-functions over $S$-integersPro-$\mathbf H_p$ density in the free group of rank two: a Frobenian criterion on the mod-$p$ torusProof of the positive trace gap conjectureOn the DML(1) property for regular endomorphisms of affine spaces: the $\mathbb{G}_m$-caseCongruence Classes in $\mathbb{F}_p^2$: Sharp Results via an Energy ApproachDisproof of a Conjectured Upper Bound for the Davenport ConstantTotal rings of quotients of higher dimensional Iwasawa algebrasA computable wandering and tracelike vector for modular orbits in the Bergman spaceHigh Rank and Multiplicity in Random and Perfect Profinite GroupsFrobenius 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 proofGalois-Orbit Structure, Ramanujan Sums, and Stable-Range Collapse for Cyclotomic Cosine Formulas$A_2$-frames, negacyclic glue, and extremal strongly $6$-modular latticesThe number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular varietyDefinability and undecidability via the torsion subgroup of unitsCompleted cohomology of Hilbert modular varieties below middle degreeGeometric lifting and Freiman's $3k-4$ theorem in compact connected abelian groupsA proof of the Baruah--Gogoi conjecture on sums of odd and even overlined partsInfinite families of pairs of real quadratic fields whose class numbers are divisible by a given integerDefinite integral Albert algebras: arithmetic and finite geometryModular integrals for individual modular knotsConstruction of vector-valued adelic automorphic formsZero density estimates for $\mathrm{GL}_2$ automorphic $L$-functionsGevrey localization for simple and distinct zeros in a prime-modulus Dirichlet familyAn Approximate Version of Vu's Theorem on Economical Subbases For Non-Integer ExponentsShifted log-sine integrals and multiple zeta valuesMorse Topology, Zero Products, and Elliptic Prime CrossingsOn some $D(u^2)$-triples and quadruples of triangular numbersBeyond the unique pair: a two-parameter family of rational triangles with equal perimeter and areaThe Arithmetic of Reducible Rank 2 Hypergeometric MotivesAn Introduction to the Lagrange and Markov Spectra through the Lens of Generalized Markov NumbersWeighted bilinear identities and supercongruences for Ap\'ery-like polynomialsOn the hyperbolic prime number theoremDistinguishing Gauss sumsA tyro's approach to the tilted sieve: beyond the Erd\H{o}s--Rankin boundCounting $k$-tuples of positive integers such that the values of several polynomials of $k$ variables are relatively primeRankin-Cohen Pairings and Hilbert Hecke Eigenform Product IdentitiesOn the monomials of Poincar\'e Series of negative indexTrivial zeros of zeta functions of type $\mathrm{A}_r$Delta Characters and Filtered IsocrystalsOn the distribution of the minimal length of addition chainsA Szemer\'edi-Trotter Theorem in Arbitrary FieldsThe intersection of local Arthur packets for even orthogonal groups and applicationsA minimal HRT counterexample at the sharp Gelfand--Shilov thresholdResultant 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 fourfoldsLocally analytic representations in mixed characteristic via stacksEndoscopic liftings and parameters of epipelagic representations for classical groupsEvaluating $\mathrm {SU}(3)$ Verlinde sums using spectral graph theoryComputation 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 OneCarmichael 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 studyAn Integral Representation of the Generalized Fibonacci NumbersBrauer-Kuroda relations for ramified graph coversThe Sphere Packing Problem in Dimension 4 and the Twenty-Four-Cell ConjectureMoulds, Bimoulds, and some Lie algebrasA density version for the sum of nine cubes of primesOn the Euler transform and the floor functionDistinct exponents in the prime factorizationIrreducible polynomials with restricted digits in base $b(T)$On the generation of multiplicative groups by small primesThe density of sums of distinct divisorsDensity of large holes among power-free lattice pointsA surprising generalization of the M\"{o}bius functionS-integrality for families of ordinary K3 surfaces and algebraicity theoremsOn the positivity of truncated pentagonal number series and some conjectures of MercaIrrationality Exponents and Partial Quotient Growth in Continued FractionsAbelian $p$-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 regularThe weighted large sieve through ParsevalLarge values of the Hurwitz zeta function with rational parameterEqual subset sums and close divisorsBoyd's conductor-11 Mahler measure conjecture: proof of the split-integral identity (C3), with an exact structural analysis of the family S_kA certified continuation machine for Mahler measure identities at CM points, with twelve new proofs of conjectures of SamartPeels of Equilateral Triangulated SurfacesOn two families of period integrals related to Catalan's constantImproved rational approximations to Catalan's constantCokernels of random $p$-adic orthogonal matrices and their linearizationsIterated integrals for generalized Appell functionsA 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 periodsRemarks on the Geometry of Sets in $\mathbb{Z}^d$ with Small Fourier $L^1$ NormThe existence and uniqueness of magic-faced hypercubes, and applications to Khajuraho most-perfect magic squares, cubes, and hypercubesThe Odlyzko-Poonen Conjecture on Irreducibility of Random PolynomialsExtreme values of central $L$-derivatives and heights of Heegner pointsA finite arithmetic form of Robin's inequality and its equivalence to the Riemann hypothesisAn irreducible decomposition of the Weil representation restricted to open compact subgroupsThe unique extremal threemodular lattice of rank 26, the generalized hexagon $(2,8)$, and the tight Cayley-plane $5$-designApproximating Pi (and other constants) by Radicals in the Footsteps of Rabbi Abraham Ibn Ezra and Guru RSJ ReddyErgodic Averages over Shrinking Sectors of $\mathbb Z[i]$Continuous Optimization for p-adic ModelsZero-Run Spectra of the $(3,2)$ Raney numbers Modulo PrimesEisenstein scattering and Plancherel decomposition on cuspidal Bruhat-T**s quotientsResultant of an equivariant polynomial system with respect to a direct product of $r$ symmetric groupsSupport-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 PolynomialsIwasawa theory of class field towersA quadratic-residue dichotomy for two partition functions modulo 3On periods of the Tribonacci sequence modulo primesMonogenic Fields of Cryptographic SizeBad Reduction of Genus Two Curves with complex multiplicationAlmost Trivial Units in Group RingsZero density theorems for short intervalsMaximal Unramified $p$-Extensions with Prescribed Galois Groups: A Quantitative Refinement of Ozaki's TheoremOn a Tur\'an's theorem for small primesOn a Tur\'an's theorem for arithmetic progressionsRomanoff type theorems for polynomials over finite fieldsSteinness of the Basic $\mathrm{GL}_n$ Local Shimura Tower in Odd RankOn $\mathbb{Z}_2$-extensions of real quadratic fields with class group of $2$-rank threeCounting number fields with symplectic Galois groupThe variance of the number of lattice points in narrow sectorsExplicit bounds for the prime number theoremWave Numbers: Discrete Sequence Algebras, Sieve Projectors, and Dynamical Geometry$v$-adic Chowla-Selberg formula over function fieldsCritical Pairs for Mixed Restricted Sumsets in Prime FieldsA two-step supercongruence for an Ap\'ery-like sequenceLarge values of quadratic Hecke $L$-functions with prime-related moduli of the Gaussian fieldLower-order terms in mean-square formulas for the Euler--Zagier double zeta-function and regularized multiple zeta valuesHigher Reciprocity, Cassels Pairings, and Selmer Towers for the 3/5 Congruent Number ProblemRefined sum formulas for finite multiple zeta values of level twoTwo Legendre-symbol determinants of Sun and Bernoulli numbersConcave transforms and volumes of adelic line bundlesSelmer groups of CM-twists of elliptic curvesInterpolation determinants and the Lebesgue--Nagell equation $a^2-D=b^p$On the noninjectivity of Jordan's totient functionsDetecting split surfaces, RM surfaces, and minimum walks on isogeny graphsNon-Archimedean Poincar\'e series and geodesics on the Bruhat-T**s treeThe exceptional set of a prime and a squareOn existence of generalised Lehmer numbers modulo primesImaginary Non-CM Fields of $2$-Power DegreeA fully faithful p-adic Riemann--Hilbert functor for filtered coherent D-modulesProofs of eighteen conjectural identities related to the modulo nine Kanade--Russell identitiesSharp zero estimates for trajectories of polynomial vector fieldsProportions of the non-trivial zeros of the Riemann zeta functionSelberg sieve weights and sign changes of Kloosterman sums. I. Uniform asymptotics for shifted weightsSelberg sieve weights and sign changes of Kloosterman sums. II. Square-free moduli with at most four prime factorsOn the abundance of rigid meromorphic cocycles for quadratic forms in four variablesThe lower bound of shifted primes with large prime factors$D$-elliptic modular curves $X_0(N)$Asymptotic Behavior of Iterated Sets of RemaindersWeighted Generalizations of Zagier's PhenomenonThe local Dold congruence for Fibonacci and Lucas sequencesOn Normality Preserving OperationsGeometry around unramified CM pointsAlgebraic independence of periods of Anderson modules and their hyperderivativesExceptional maps and abelian points in backward orbitsA polynomial basis for the multizeta algebra in positive characteristicAbelian dynamical Galois groups over global function fields$\Kab$ has the Bogomolov property for canonical heightsThe Hall-Janko Simple Group and the Icosian Leech LatticeExtremal Least Common Multiples in Rows of Pascal's TriangleExistence of a Hall ray in higher dimensional Lagrange spectraSum of Three Squares and Particle in a Cubic Box - DegeneraciesQuantum modularity in refined topological recursionFundamental Lemmas in Universal ResolutionFrom Dimension Drop to Aperiodic OrderDensity 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 latticesExtreme value laws for intrinsic Diophantine approximation on spheresEigenvectors of $p$-Curvature for Geometric Difference EquationsGalois deformation rings and modularity in the residually reducible caseOn The Cyclicity of Algebraic LatticesThe large sieve for square moduli under Hooley's hypothesis $R^*$Annular Frobenius Classification of p-adic Stieltjes--Schwarzian EquationsThe integer group determinants for $\mathbb{Z}_p^n$Difference of the Sum of All Odd and Even Overlined Parts of OverpartitionsFrobenius Numbers Associated with Primitive Pythagorean QuadruplesArithmetic structure of $L_2$-norms of ${\mathrm{SL}}_2(\mathbb{Z})$ matricesA Note On Certain Minimal Excludants Over OverpartitionsOn low-discrepancy sequences and Poissonian pair correlationHigher Labute-Serre duality and Lyndon wordsNon-existence of sets with few special directionsReal quadratic fields and finite quantum dilogarithms I$\mathbf{Bad}(\mathbf{r};\mathbf{s})$ is Hyperplane Absolute WinningAn equivariant version of Gabber's lemmaOn 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 partsA new family of maximal curves not covered by the Hermitian curveSimultaneous nonvanishing of quadratic twists via Rankin-Cohen bracketsFinite subgroups of outer automorphism groups of the absolute Galois groups of mixed-characteristic local fieldsNorms of Schneider--Teitelbaum Polynomials in $p$-adic Fourier TheorySampling and Moments of Reciprocal Quadratic Mellin IntegralsOn a question of Ruzsa about densities of sumsetsA characterization of Sophie Germain primes - IIThe Three Gates: A Rooted-Operator Approach to Weil PositivityA problem of Yang and Chen on weighted representation functionsLow moments of automorphic random multiplicative function sumsFinding New Limit Points of Mahler Measure by Methods of Missing Data RestorationComputational results on sums of a prime with squares or cubesRogers--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 setsOn 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 fieldsInfinite prime sumsets in structured and $U^k(\Phi)$-uniform setsConductor-Discriminant Inequality for Tamely Ramified Cyclic Covers IConductor-Discriminant Inequality for Tamely Ramified Cyclic Covers IILogarithmic--exponential preparation in sharply o-minimal structuresCombinatorics of hyperplane arrangements and Witten zeta function at the originMorphism spaces on low degree hypersurfaces

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/2026-09-17/ Distinct Consecutive ProductsTranscendence measure for the values of the logarithmic derivative of the Bessel function $J_0$ at algebraic argumentsLattice points close to a smooth curve and squarefull numbers in short intervals. IIEffective Hecke eigenvalue equidistribution over the Atkin--Lehner subspacesOnly finitely many modular Jacobians are supersingular modulo a given primeOn two forms in many variables of different degreesZero-Density Concentration for Dirichlet PolynomialsUnramified Geometric Iwasawa theory of function fieldsSurjectivity of the Enots Wolley SequenceContinuous approximation to the reciprocal sum of the cubes of Fibonacci numbersExact universal normalizations for the G\'al--Koksma lemmaNonvanishing of ray class $L$-functionsA $q$-recurrence for a finite Ap\'ery limitGraded Algebras of Modular Forms and Sign Changes of Fourier Coefficients for Eta QuotientsBounded intervals containing a given number of primesExtreme Values of Quadratic Dirichlet $L$-Functions over Monic Irreducible Polynomials in $\mathbb{F}_q[t]$Cyclotomic Prime ExtractorsPeriodicity conjectures for all 2-sumfree sequencesExtreme values of Euler-Kronecker constants of cubic abelian fieldsStable Trace Formula for Newton strata of Shimura varietiesOn Multiple Eisenstein Series in Positive Characteristic: Direct Sum ResultOn a conjecture of Browning and Sawin on random hypersurfaces with sign coefficientsA uniform effective Andr\'e--Oort resultAn Omega result for partial sums of the Riemann zeta function$\Omega$-results for the logarithmic derivative of $\zeta(s)$ on vertical homogeneous progressionsArithmetic Constraints and Limit Laws for Diagonal Rational PartitionsFinite Fourier Duality, Radial Values, and Arithmetic of a Mod Eight False Theta QuotientTranscendence criteria for the minimal word of the rational base $3/2$Tunnell-type criteria for variants of the congruent number problemExplicit equations of Galois subfields of Hermitian function fields with respect to decomposition groupsThe non-spherical sup-norm problem for $\mathrm{GL}(n)$ and generalized spherical functionsTwo proofs of the Cassels--Swinnerton-Dyer conjecture for cubic surfacesGeneralized DCCQ: From Binary Quotients to Multinomial Simplex Geometry and Critical-Strip CoordinatesOn the singularities and the Kodaira dimension of unitary Shimura varietiesA somewhat sure note on an un-Schur problemGraph lattice sums and graph zeta functions for long-range interacting quantum lattice models

arXiv math.NTの新着論文38本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-16/ The Waring-Goldbach problem in short intervals under the Generalized Riemann HypothesisMean Lindel\"of Hypothesis and Prime Geodesic Theorem on Bianchi ManifoldsA formula for the rank over $\mathbb{Q}(t)$ of the elliptic curve $y^2=x^3+At^6+Bt^3+C$Number fields as curves over $\mathbf{F}_1$Simultaneously small continued fraction entropy and base $b$ entropyElementary proofs of congruences modulo 5 for overpartitions with restricted odd differencesRational Points near Monofractal Curves and the Strong Oscillation PrincipleLocal Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrizationLocal Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrizationTwisted Rational Zeros and Local-Global Principles for Linear Recurrence SequencesHigher Schwarzians of Elliptic Double Covers and Eisenstein--Kronecker FunctionsThe Furstenberg-S\'ark\"ozy theorem for sums of an even number of odd powersAn infinite family of imaginary biquadratic fields with a large class numberLaurent series expansions for the Barnes multiple zeta functionTriple divisor type functions in arithmetic progressions to prime power moduliIwasawa theory of (directe) Cayley graphsThe Local Ghost Theorem in the Tr\`es Ramifi\'e CaseDistribution of squarefree integers with double congruence conditionsPrime-power congruences for level-one eigenformsExtreme values of quadratic Hecke $L$-functionsOn $t$-sumfree sequencesMixed moment of $GL(2)$ and $GL(3)$ $L$-functions in the level aspectAn additive problem in connection with some quadratic real fields with class number onePowers of the Thue--Morse Series: 2-Adic Valuations and Automatic Odd PartsRefined conjectures on Fitting ideals of BDP Selmer groupsModular functoriality for finite groupsUniform Mordell-Lang conjecture for semiabelian varietiesA class formula for effective Anderson motivesOn Sarnak--Str\"{o}mbergsson conjectureImproved bounds for Szpiro's conjectureEven-degree Hermitian Ikeda lifts via Fourier-Jacobi descentHypothetical connection of the theta functions of Dirichlet characters with the real cyclotomic fieldsLoop spaces, twistor $\mathbb P^1$ and tempiric parametersList Decoding, Linear Hashing, and Furstenberg over $\mathbb{F}_q$Block-count constrained harmonic sums: spectral expansion and block-directed Euler-MaclaurinOn a classical zero-sum invariant II: Disproof of a long-standing conjectureSmall degree isogenies between conjugate principally polarized superspecial abelian surfacesA perimeter analogue of Franklin's identity and an inequality related to the parity of parts

arXiv math.NTの新着論文69本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-15/ The Strong 24-ConjectureTheta functions after WeilDynamical uniform boundedness for unicritical polynomials and elliptic curves of large rankArithmetic Siegel-Weil for the spherical Hecke algebraGalois representations and modularity for twisted moments of Kloosterman sumsPointwise ergodic theorems along sequences of intermediate growthSpherical statistics and phase transitions in high-dimensional latticesFiniteness of an Isogeny Class via EquidistributionPrime and Nonprime Totatives: A Sharp Construction and Exact ThresholdsThe optimal scale in Linnik's microsquare problem for almost all integersGeneralized Wieferich primes and monogenic polynomialsDensity of Vanishing of Certain Eigenspaces of Cyclotomic Class GroupsA Local Proof of Langlands's Second Main Lemma for Local Epsilon Factors over Nonarchimedean Local FieldsModular and Shimura curves $X_0^D(N)$ embedded in $\mathbb P^1 \times \mathbb P^1$Reduction of integer tiles via CRT and base-p digitsPatterns in the Markov numbers and their generalizationsQuantitative linear independence for square rootsTwisted Lubin-Tate Big Witt Vectors and Fleck-Sun-Wan CongruencesOn Decomposition of Drinfeld cusp forms of level $t$Golden-ratio growth of Conway's subprime closureTwo-Height Approximation and Mahler's Problem on Liouville NumbersA Central Limit Theorem for Coprime Pair Counts in Randomly Translated DisksSurjectivity of Finite Rank-Capped Enots-Wolley SequencesThe Jensen--P\'{o}lya program and inequalities for arithmetic sequencesCubic AGM graphs and Hessian $3$-isogenies over finite fields $\mathbb{F}_q$ of odd characteristic with $q \equiv 2 \pmod3$Character sums on an oriented singer conic and explicit Ramanujan double coversAn explicit power-saving bound for S\'{a}rk\"{o}zy's Theorem on shifted primes, assuming GRHBloch cycles and the weak two-variable Chinburg conjectureDynamical generalizations of Chowla's conjecture on short averagesElimination of Ren\'e Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid ProblemAsymptotic Formula for Biregular OverpartitionsCritical Restricted Sumsets at the Boundary $\lvert A\rvert+\lvert B\rvert=p$Prime Plus a Non-Square-Free Integer: An Elementary ApproachTranscendence of Montgomery Reduction Factor in the Ring of Integers Modulo Infinitely Large PrimesA proof of Sylvester's conjectureThe typical size of Hecke eigenvalue sums is $o(\sqrt{x})$Two-term dilogarithms, mixed-base Nahm sums, and Fricke symmetryEkedahl-Oort strata meeting the supersingular locusLaurent coefficients of Zagier-type zeta function {\`a} la Ishibashi and arithmetic aspects of extended Ramanujan period functionThe Dynamical Mordell--Lang Conjecture for Relatively \'{E}tale Systems over Products of CurvesOn the largest prime factors less than $y$ of consecutive shifted primesAlgorithms for $p$-rationality and for $p$-saturation of unitsAlgebraic independence of the exponential and Weierstrass $\wp$-functionsOn the arithmetic of Tate-Shafarevich groups via Kolyvagin's conjectureOptimising Selberg's method for critical zerosOn the number of solutions to $S$-unit equationsHecke structure of quaternionic modular forms mod $p$Periodicity and Period-Length Bounds for Browkin $p$-Adic Continued FractionsAn extension of algebraic independence of special values for non-lacunary power seriesLong runs of integers with small prime factors and the divisor function of $n!$A Construction of an Extremal Even Unimodular Lattice of Rank $88$Singular automorphic products and BKM algebrasA septic covariant and the Hermite--Joubert problem in degree sevenAnother proof of the $U^4(\mathbf{F}_p^n)$-inverse theoremCauchy laws for zeta logarithmic derivatives and stationary Stieltjes transformsLow moments of Hecke eigenvalue sumsA lattice family with kissing constant $\tau(\mathcal{L}_n) \ge e^{\sqrt{n}}$Zeros in The Character Table of The Wreath Product of The Symmetric GroupMatrices over non-commutative rings as sums of fifth and seventh powersSubset-Sum Density Realization in Locally Finite Abelian GroupsTorsion, Betti rank, and small points in semiabelian schemesThresholds and Fluctuations for Colorful Arithmetic Progressions in Sparse Random ColoringsNoether's problem for $A_6$ and $A_7$Growth beyond exponent $3/2$ for convexity and iterated sum setsAKE principles in roughly deeply ramified henselian valued fieldsAlgebraic Structures on Sets of PartitionsNP-hardness of ideal lattice problemsGeometric realizations of Brauer classes on K3 surfaces from hyperk\"ahler contractionsDynamical Mordell--Lang Conjecture for Higher-Rank Radially Ramified Skew Products

arXiv math.NTの新着論文25本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-14/ An adelic approach to the Kudla-Millson lifts over totally real number fieldsLocal-global principles for visibility of lattice points on parameterized curvesOn the variation of slopes over moduli stacks of Galois representationsCritical convergence and Hausdorff measures for generalized Flint Hills series$S_h$-sets in abelian groupsA Generalization of S\'ark\"ozy's theorem in function fieldsZeros of Quasimodular Forms Defined by Iterated SumsThe first moment of quadratic Dirichlet $L$-functions in the even hyperelliptic ensembleTight universality of $m$-gonal forms with minimal criterion setsGauss Genus Theory in Characteristic 2Projective Kernels and Replicability in Modular Function TheoryClassification of torsion of elliptic curves over quintic fieldsLarge fluctuations of extended Rademacher random multiplicative functionsProjection and fibering in groups of bounded exponentKronecker sequences beyond the torus: nearest-neighbour distances and best returnsIwasawa theory of CM elliptic curves at potentially supersingular primesKolyvagin's conjecture at non-ordinary primesAn asymptotic formula for a cubic moment of $GL_2$ $L$-functionsJacquet--Rallis transfer for GL(2)Quasipolynomial density bounds for $K$-point configurations in $\mathbb{Z}^d$Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued FractionSerre's problem on statistics of Brauer symbolsPoincar\'e duality for pro-\'etale $\mathbf{Q}_p$-local systemsCharacteristic Classes of Adelic Vector Bundles and ApplicationsNon-archimedean Monge-Amp\`ere measures for toric metrics on subvarieties of toric varieties