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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/2026-10-22/ An Asymptotic for Non-Wieferich NumbersA Counterexample to the Eventual Stability ConjectureSch\"affer's conjecture for even $k \le 42$A quaternary Diophantine inequality with prime numbers of a special form (II)A relative Schinzel-Zassenhaus bound for the polynomial $T^2 - 1$Short sums of the M\"obius function over function fieldsSubset sums of power values over Galois ringsOn a conjecture of VelaniHecke Orbits on Globally Drinfeld-Uniformized Shimura Varieties Are $p$-adically Nowhere DenseThe Octonionic Rational Wave Numbers: Non-Associative Sequence Algebras, Moufang Loops, and Exceptional $G_2$ SymmetriesZeros of quadratic Dirichlet $L$-functionsConstruction of Galois modules describing ideal class groups and applications to Iwasawa theoryMixed sums of infinite multiple zeta-star values with restricted indicesStatistics of entries of matrices from the general linear group over a finite fieldIdeal class groups of certain real quadratic number fields and factorizations of values of certain quadratic polynomialsComputing Theta Characteristics and their Galois action on general curves of moderate genusThe exceptional set of Goldbach numbers within the set of squaresResidue Sums Modulo Products of Two Distinct Odd PrimesPerturbing the Conway sequenceOn the Gauss sphere problemSharp spherical $L^p\to L^4$ extension estimates over finite fields in odd dimensionsInteger symplectic matrices in expanding boxesIntegral trace forms of cyclic number fields without tamenessOn the notion of reasonable functions in Cohen--Lenstra type heuristicsSquarefree values of random polynomials are Gaussian mixturesA Sharp Bound for Additive ComplementsZeros of $E_2$, quasi-periods, and Schwarz mapsSupport periods of polynomials and support-primitive decomposition of constacyclic codes over Galois ringsLocal Gan-Gross-Prasad conjecture for unitary groups: Trace formula approach for epsilon dichotomyHomological branching laws for $p$-adic and mod $p$ representations of ${\rm GL}_2$ over a $p$-adic fieldHigher rank spectral projector estimates and a Stein--Tomas restriction theoremOn Almost MDS codes holding $(n-k-1)$-designs and an open problem on Witt designSolutions of $x^\alpha+y^\alpha=1$ in $\lambda$-Cantor setsLinear Complementary Pairs of MDS Codes from Elliptic CurvesPainlev\'e representations for joint moments of characteristic polynomials from the orthogonal and unitary symplectic groups

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/2026-10-21/ Galois Groups of Shifted Exponential PolynomialsClass polynomial obstructions to canonical congruences for the smallest parts functionSmall sums of roots of unity: polylogarithmic exceptional sets and conditional separationUpper Bounds on the de Bruijn-Newman constant for Dirichlet $L$-functions with primitive real-valued charactersThe Projective Reed-Muller Code from Quartic Curves in the Projective PlaneQuantum Variance for Hecke--Maass Cusp Forms on the Vertical GeodesicBowen--Franks groups and minus class groups of imaginary abelian fieldsNon-vanishing of central values of angular Hecke $L$-functionsOn a Notion of Density Related to Restricted Diophantine ApproximationAn Equivariant Main Conjecture for Branched $\mathbb Z_p$-Towers of Finite Graphs and ApplicationsSmall values of the Riemann zeta-function near the critical lineA determinant formula for multiple harmonic sums and their linear independenceDense Sets with Prescribed Difference Representation FunctionsNew Directions in IrrationalityWeyl Bounds for $\operatorname{GL}_2\times \operatorname{GL}_2$ Rankin--Selberg $L$-functions via Short Spectral MomentsPrimes in short intervals assuming the Riemann hypothesisPost-quantum commutative group actions from oriented superspecial abelian varietiesTheta RelationsSEAC from EAC modulo Schanuel: reduction to algebraic exponentialsUncountably many settled elements are never Frobenius elementsOn the average of class numbers of indefinite binary quadratic formsIrrationality exponents of logarithmic numbers: Values, quotients, and graded approximationSimultaneous visibility in cut-and-project setsEuler systems for self-dual Hecke characters over biquadratic fields with applicationsSimultaneous popular differences for polynomial and linear progressions in finite fieldsA necessary condition for a Romanoff type theoremA Joint Local Limit Theorem for Prime Divisor Counting FunctionsUnconditional Subexponential Arithmetic Circuits\ for Positive Factorial MultiplesSmall and large gaps between zeros of Dirichlet $L$-functionsBorel's computation of the ranks of $K$-theory revisitedGeneric distinction of induced representations: the case of symmetric spacesA cut-and-project set which is not bi-Lipschitz equivalent to a latticeRational analytic prismatizationSupercuspidal blocks and the local Langlands correspondenceThe stacky approach to de Rham-Witt cohomology

arXiv math.NTの新着論文60本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-20/ Ramanujan Conjecture and Riemann Hypothesis for the unitary groups over function fieldsGaps for PLRS with zero coefficientsDihedral fields with Bloch lattice index five and quadratic subfield Q(i)Recovering Dirichlet coefficients from even samplesDiamond Maximal Operators: Classification, Moduli, and Oscillation EnvelopesOn the Ramanujan-Ligozat modular unitThe exact Euclidean window of $\mathbb{Z}[\sqrt{14}]$Markoff spectra of Hecke groupsPillai's equation between k-generalized Pell numbers and Tribonacci numbersStevens' Approach to Kloosterman Sums on Split GroupsHuman Exposition of Claude's 2/3 Theorem on the zeros of zetaInverse trigonometric and hyperbolic identities,series and products for Lucas sequencesOn reducible $\ell$-torsion representations of Picard curvesDouble shuffle and naive duality for multiple Dirichlet seriesAll totally real abelian number fields of class number one are EuclideanLarge values of derivatives of quadratic Dirichlet $L$-functionsThe 3-adic Steinberg block and a categorical 3-adic local Langlands correspondence for $\text{GL}_2(\mathbb{Q}_3)$Graded Structures of $v$-adic Carlitz Multiple Polylogarithms and $v$-adic Multiple Zeta ValuesA sharp lower bound for $h$-fold restricted sumsets of integersCovering finite fields by translates of multiplicative subgroupsLucas' Theorem modulo $p^n$ via Harmonic sums$2$-adic Representations of Elliptic Curves over $\mathbb{Q}_2$Mixed Tate Chabauty--Kim beyond the polylog quotientDistinctness and Algebraic Degrees of Inverted Kloosterman SumsHeights of small CM cycles on Unitary Shimura VarietiesThe factorial separation conjectureOn The Manin ConstantRational Points on Drinfeld Modular Curves of Prime LevelFrobenius Profiles of Polynomial-Multiple MRD CodesA Fourier expansion principle for coherent cohomology of powers of Tate curvesAsymptotic low slopes of toric exponential sumsOrders in the Euclidean CourtHalf-sized gaps between zeros of the Riemann zeta functionOn Carmichael Numbers Constructed from Consecutive Jacobsthal NumbersPellarin Values from Cauchy Coordinates on Arbitrary CurvesOn Special Arithmetic Gamma Values and Thakur's Gauss Sums: From $\infty$-adic to $v$-adicFrom Inverse Vandermonde Matrices to the Shift Structure of the Dirichlet Eta and Beta FunctionsSign bias in hyperbolic double cosetsPasten's arithmetic derivatives and the decomposition into gainsThe density of discriminants of $A_4$-quartic fieldsThe irrationality exponent of the lemniscate period: A determinant proof with a Lean 4 formalizationOn multilinear forms for mod \(p\) representations of \(\operatorname{GL}_2\) over a \(p\)-adic fieldSurfaces Associated to Zeros of Automorphic $L$-functionsUniform lower bounds for the average length of finite Pierce expansionsEisenstein series for orthogonal groups and Kneser neighboursThe Riemann zeta function at the zeros of real-rooted trigonometric polynomialsThe sum-product conjecture holds for fixed-field lattice product constructionsFourth moments of prime exponential sums and exceptional sets for sums and differences of primesAn Exotic Congruence for Irregular Weight Picard Modular FormsZero-free half-planes for Hecke L-functions over number fieldsIsolated zeros of the Riemann zeta function and zeros of linear combinations of Dirichlet $L$-functionsLocal Converse Theorems for $k$-Middle Supercuspidal Representations of $p$-adic $\text{GL}(kn)$Inverse Zero-Sum Problems: The Property C and Property D ConjecturesProjective Decomposition and Intersection Cohomology of Rigid SpacesThe Corners of Ramanujan: Partial- and False-Theta Companions to Third-Order Mock Theta FunctionsTorelli theorem for the moduli spaces of twisted vector bundles on smooth projective curvesCharacteristic cycles and non-acyclicity classes for constructible \'etale sheavesGauss-Manin connection in disguise: limiting periods and quasi-Jacobi formsMillicharged particles and the degree-3 Prouhet-Tarry-Escott problemAmpleness of non-symmetric line bundles on degenerations of abelian varieties

arXiv math.NTの新着論文34本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-19/ Space-filling curves and small-ball probabilities for the Kloosterman processA Non-Split Motohashi Formula for Toric Periods over Number FieldsDensity Bounds in Hua's Theorem for Prime SquaresGalois Groups of Trinomials with Small CoefficientsPoisson-Dirichlet statistics for the log-modulus of the Riemann zeta function on expanding intervals near the critical lineMetric Poissonian Pair Correlation Property Part 2: The Case \(n\log n\)Metric Poissonian Pair Correlation Property Part 1: The Case \(n+\log n\)Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta FunctionImproved explicit Burgess-strength bounds for composite moduliArithmeticity of critical $L$-values for Hilbert-Siegel modular forms in the left half plane and $s = 1$Zagier's 2-3-2 formula for multiple Eisenstein seriesMinimal asymptotic \(g\)-adic bases from arbitrary partitionsA $\mathrm{GL}_3$ level analog of Selberg's result for $S(t)$Note on the largest prime factors of consecutive integersImproved $L^p$ maximal estimates for higher-degree Weyl sumsMahler Method and Vanishing TheoremMore than 8/9 zeros of the Riemann zeta function are simple or on the critical lineLifting mod $p^n$ Galois representationsOn a series related to the M\"obius functionFourier dimension for exactly approximable matricesCuspidal Class Number Formulae for Intermediate Modular Curves of Prime LevelConfluence relations, Hoffman basis over \mathbb{Z}_{(2)}, and the Deligne--Drinfeld conjectureThe distribution of $\alpha p$ modulo one in real quadratic function fieldsNear optimal gap in the Lonely Runner ConjectureA duality principle for the neighbourhood of manifolds and applications to counting rational points near curvesA $p$-adic Riemann--Hilbert correspondence over Robba ringsA Simple Proof of I. Chowla's Theorem on Addition of Residue ClassesPresentability of categories of localizations and analytic ringsRational Area Profiles of Regular Polygons Cut by Two Congruent DiagonalsWhittaker Functionals for Exceptional RepresentationsSeven ordered points and the nonexistence of arithmetic ball quotient compactificationsWeighted configurations and the nonexistence of arithmetic ball quotient compactificationsBrauer-Manin obstruction for symmetric powersOn the asymptotic growth of the norm of the partial sum operator on $\mathscr H^1$

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/2026-10-16/ 86 unknowns for Hilbert's tenth problem over the rationalsMixed moment and joint non-vanishing of $\mathrm{GL}(3)\times\mathrm{GL}(1)$ and $\mathrm{GL}(1)$ $L$-functionsEhrhart Polynomials of Triangles in $\mathbb{R}^3$On the Diophantine equation $X^2+p^m=p_1^{n_1}p_2^{n_2}$CM Elliptic Analogue of the Coleman--Ihara FormulaA simpler proof that there are no Landau--Siegel zerosOptimal Reduced Representatives of Quadratic APN Permutations in Odd DimensionExplicit reduced APN permutations: ramification and optimal Galois-ring liftsNon-vanishing mod $p$ of derived Hecke algebras of multiplicative groups over number fields, IIModularity criteria for multiple Eisenstein seriesOn the dimension conjecture for global Galois deformation rings in characteristic twoSmoothness of Shortest Isogenies to Frobenius ConjugatesImaginary quadratic fields of class number at most 2000Frey-Mazur theorem for semistable elliptic curves over function fieldsLocal Tate duality for syntomic cohomology in positive characteristicA prime plus a square: A conditional 11/20 upper boundA New Bound for the Gauss Circle ProblemA number field extension of Ramanujan's identity and its integral representation via the generalized Riemann $\Xi$-functionTwisted Artin-Schreier Theory I: $(C_p \rtimes C_{p-1})$-extensions of local function fieldsIsaac's Condition (TU) is falseA variation on local trilinear formAn introduction to algebraic groupsOn the Sampling of Certain Dirichlet and Prime Sums at Gram Points and their ViscosityClassification of vanishing fusion rings of rank fourEkedahl-Oort strata with a superspecial factor in unitary Shimura varietiesLogarithmic exponential sums with multiplicative coefficientsThe discrete second moment of the Riemann zeta-function along powers of Gram pointsVariation of Shafarevich-Tate groups in Hida familiesAutomorphic Dirac Operators and an Analogue of the Quantum Harmonic Oscillator on $\Gamma \backslash \mathfrak{H}$On exponential sums with multiplicative coefficientsA counterexample to a conjecture of Plotnick on knot exteriorsLocal Extrema and Infinite Derivatives of the Delange Function of Base 3Density of repelling periodic points for cubic rational mapsGeneralized Erd\H{o}s--Ginzburg--Ziv Constants for finite abelian groups of rank threeThe $L\log L$-Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of DimensionalityB\'ezout bounds and rational points on quasianalytic graphsAn undecidable problem in dynamicsUnimodular Zeros of Selmer's Harmonic TrinomialsDouble covers of tori for p=2 and genuine functions

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/2026-10-15/ On digit-appending walks along linear recurrencesLarge value estimates for Dirichlet polynomials and trilinear sums over short intervalsOrthogonality relation between $GL(3)$ coefficients and additive characters with linear and non-linear phasesSome Bounds on the Lehmer IndexElliptic curves attached to Jacobians with imaginary multiplicationA new way integral for the $n$-fold cover of $SL_2$An algebro-geometric approach to profinite iterated monodromy groupsA Bounded-Defect Construction for the Mondrian Art ProblemReductions of Galois representations of slope $2$Zero-cycles and Brauer groups on certain Enriques surfacesTernary polynomial relations and periods of cusp formsShapes of tame abelian number fieldsA folklore conjecture on multiplicative exponential sumsArithmetic Visibility in Polygons: Curved Sight in the Art GalleryOn a problem on partitions into distinct primesThe Density and Quantitative Upper Bound of Integers Not Expressible as the Sum of a Prime and a Zumkeller NumberOn the Erd\H{o}s--Odlyzko--S\'ark\"ozy conjecture for prime-power moduliDivisibility Estimates for Gaussian Norms and Almost-Prime Orders of a CM Elliptic CurvePrimes between 8th powers?Conguences for Odd Unimodal Sequences and a Problem of Bringmann And LovejoyIntegral Specializations of Polynomials: Hilbert Irreducibility, Coprimality, and DensityNew bounds for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ shifted convolution sumsGenus character $L$-functions of orders in quadratic function fieldsOn the Hardy--Littlewood--Chowla conjectureAn upper bound for valuations of elliptic nets at primes of bad reductionQuantitative lower bound for Pythagorean pairs in boxes of prime powersS-squareful values of binary quadratic formsGCD and ABC inequalities for abelian varieties over function fieldsUniversal norms of partially de Rham $B$-pairs and perfectness in Lubin--Tate Iwasawa theoryThe large sieve inequality and additive decompositions of sums of squaresArithmetic Siegel--Weil formula on the product of modular curvesThe existence of small defining polynomials for number fields$\ell$-Independence, slopes, and weights of $\ell$-adic cohomology groups of rigid spacesSymplectic extension graphs and Ribet's lemmaPositivity and negativity for $h$-bases for $n$Proofs and disproofs of some conjectures on zero-sum problems of new typesReciprocal Dynamics in Congruence Jumping: Integral Orbits and Valuation ConesA prismatic Riemann-Hilbert correspondenceEffective equidistribution of polynomial trajectories in $\operatorname{SL}_3(\mathbb R)/\operatorname{SL}_3(\mathbb Z)$

arXiv math.NTの新着論文117本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-14/ Counting quaternion extensions by multi-heightsGeometric bounds on norms of signed indecomposable integersWendt's determinant and finiteness of prime characteristics for permutation binomialsLinking numbers and special differential characters in arithmetic hyperbolic manifoldsSome applications of the quasi-Riemann hypothesis to class groups and small generators of number fieldsOn Permutations Whose Adjacent-Sum Reciprocals Sum to OneA Combinatorial Proof of Partition Identities for the Number of Distinct Part SizesUntrodden pathways in the study of partitions with parts separated by parityHigher rank elliptic sieve via CM endomorphismsCounting matrices with given characteristic polynomialA certified classical-strip comparison for the de Bruijn-Newman constantOn Berndt-Straub conjectures about zeros of generalized Ramanujan polynomialsA generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral ${}_2H_2$ summationFine structure of even Galois deformation ringsA recurrence in logarithmic M\"obius sums with coprimality conditions via Euler--MaclaurinYau's number-theoretic conjecture and sharp spectral bounds for quantum harmonic oscillatorsA sharp lower bound for the sextic large sieveSimultaneously preperiodic points and colliding orbits for families of polynomials in characteristic $p$The local structure of refined class groups in cyclotomic Iwasawa theoryRoth's theorem on weighted projective linesProofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_{2\ell-1}^{(2)}$Multidimensional Szemer\'edi Theorem for Pairwise Independent Jointly Intersective PolynomialsProof of a nonnegativity conjecture of Prellberg--StantonIntegral trace duality and the Witt filtration on Lubin--Tate spaceModuli descriptions of v-sheaf local modelsHyperelliptic curves on $K3$ surfacesHigher derivatives of the Gram functionArithmetic jet spaces and the unramified Zilber--Pink conjecture for subvarieties of abelian varietiesDenominators in the Farey Sequence, the Stern Sequence, and the Frobenius Problem with Relatively Prime MultipliersLikely and unlikely ramification of algebraic points on curvesAn Enhanced Higher Green's Function on the Modular CurveHolonomic sequences arising from meromorphic modular formsA Half-Constant Upper Bound for Chowla's Cosine ProblemDistribution of central values of Hecke $L$-functions of $n$-th order charactersCM fibers of Shimura parametrizations and thirteen proofs of the class number one theoremThe WZ pair and finite congruencesAutomorphisms and canonical forms of integer latticesOn Solvable Automorphism Groups of Function Fields over Finite FieldsPointwise improvement of the error term in the higher rank hyperbolic lattice counting problemSparse Lifts of q-Linearized Permutation Polynomials with Explicit InversesThe ring of values of $E$-functions is not a fieldThe Davenport constant of low-dimensional boxesBounded continued fractions and quadratic orders in $\Q(\sqrt{127})$Hecke modules associated to certain even ternary lattices of half-discriminant $\mathbf{N^2}$Stable reduction and large Nielsen orbits on generalized Markoff surfacesDynamical generalizations of the two-point Chowla conjectureA Lean formalisation of the disproof of Ramaekers's conjectureIrreducible components of crystabelline deformation rings: the wildly ramified caseWasserstein rates of all orders for the Sato-Tate law of Kloosterman sumsCohen-Lenstra heuristics and vanishing of zeta functions for superelliptic curves over finite fieldsThe Multiplicity One Defect and Congruence-Modular Exponent RatiosLow Lying Zeros of Dedekind Zeta FunctionsOn bass orders in division algebrasSquare integrable representations and Hecke eigenvalues over a local non-archimedian fieldPrivileged $\mathrm{SL}_3$-local systems are motivicp-adic Hodge theory of unipotent completions revisitedCyclotomic Structure and Exact Recurrences in Floquet Many-Body Quantum DynamicsMicrolocal Arthur packets as a quasi-canonical basis of stable distributionsThe weak cylinder conjecture for polynomial graphs of bounded degreeGalois coinvariants and fundamental groups of arithmetic schemes$2$-large sets are sets of nil-Bohr recurrenceDepth-zero local Langlands via shtukas in mixed characteristicNonarchimedean discrete groups and quasi-isometric doubles of free groupsCubic moments of eigenfunctions on surfacesZero density in short strips and short-interval bounds toward Hypothesis SNonlinear twists of Rankin-Selberg coefficients in the eigenvalue aspectIwasawa cohomology of pseudorigid families of $(\varphi,\Gamma)$-modulesA note on the $p$-adic inhomogeneous Littlewood conjecture$6$ powers of $2$ in the Linnik--Goldbach problemTribonacci numbers that are palindromic concatenations of two distinct repdigitsOn the inverse Goldbach problemSolutions of $x_1^2+x_2^2-x_3^2=D$ with small $x_3$: a spectral approachPoissonian Pair Correlation for Bernoulli OrbitsCounting subspaces with prescribed Welch sumsCoprime pairs with equal sum of divisors, assuming smooth shifted primesBloch torsion and modular combinations of Nahm sumsThe Goldbach exceptional set: an exponent 7/12 and conditional refinementA linear independence criterion for $p$-adic Hurwitz zeta values at odd integersOn the OpenAI proof that Landau-Siegel zeros do not existOn strongly minimal asymptotic bases of order $h$ generated by powers of $2$Monotonicity of Coefficients of Interpolated Multiple Zeta ValuesNon-vanishing of primitive cubic, quartic and sextic L-functionsCounting Rational Points on a Certain Bihomogeneous ThreefoldRefining the 7/8 zero-free half-plane for Hecke and Dirichlet L-functionsThe Norm Spectrum of Barnes-Wall Lattices Below Twice the MinimumBernoulli numbers and the integer group determinants of $C_p \times C_p$Post-critically finite polynomials over cyclotomic closures of number fieldsUniversal Shift Congruences for Weighted Permutation SequencesPost-critically finite polynomials in characteristic $p$Crystals and the parabolicity conjectureA trace Paley-Wiener theorem for $\mathrm{GL}_{n}(F)\backslash \mathrm{GL}_{n}(E)$, with $E/F$ a quadratic extension of non-Archimedean local fieldsDeformation and Symmetry in Two Hypergeometric SupercongruencesA quotient of the Bruhat-T**s building classifying maximal matrix orders over curvesOn Waring-Goldbach problem for two squares, three biquadratics, one quintic and one septicOn a variant of the Piatetski-Shapiro prime number theoremKitaoka's conjecture for real cyclotomic fieldsProof of Two Conjectural $q$-Supercongruences Related to Van Hamme's $\mathrm{(G.2)}$ SupercongruenceExact Rank of the Largest Good Lattice Point MatrixBounds for (k,c) model functions over p-adic fieldsExamples of Bessel Functions of Order Zero Related to the Functional Equation of the Riemann Zeta FunctionOn trace-zero norm forms of orders of rational quaternion algebras with applicationsSimultaneous Unimodularity of Positive Integer Matrices and Their Entrywise CubesSharp Constants and Extremizers in Homogeneous Tree BMOThe strong Ramanujan bound for Drinfeld modular formsOn the generalization of Christol's theorem to domains of finite type over finite fieldsPolynomial Identities for Generalized Fibonacci SequencesHow iterated sumsets grow under the assumption of small doublingOverlap distributions under the Gibbs measure of a Haar model of $\log|\zeta|$ on and near the critical lineSurvivor Set of Gauss Map with a Hole at $1$Bounds for the residue of Dedekind zeta functions under GRH and applicationsOn the calculation of an integral introduced by Hubert DelangeA lower bound for additive complements to the primesLattices with Large Kissing Number from Local DensitySchauder and Riesz Bases for Higher-Dimensional Lebesgue Spaces Inspired by ReLU Neural NetworksA series with a Cantorval set of subsums and ratio of consecutive terms tending to $1/2$ (the second Jones problem)Dynamical degrees of automorphisms of non-projective hyperk\"ahler manifoldsUniformly Bounded Orthonormal Bases of Homogeneous Polynomials on the Complex Sphere

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/2026-10-12/ On $m$-fullness in number fieldsProperness of the Cuspidal Hilbert EigenvarietyA cyclotomic gluing construction for lattice sphere packingsHankel Matrix Decompositions and Digital Sequences over Function FieldsPolynomial parametrization of $\text{SL}_2$ over global function field ringsA Rigid Analytic Curve Can Have a Dense $p$-adic OrbitA conditional bound $\Lambda\le0.13963$ for the de Bruijn--Newman constantReciprocal LCM powers and Robin's criterionReasonable bounds for Restricted Polynomial Progressions in $\mathbb F^n_p$On the Imaginary Part of $\zeta'/\zeta$Odd order cases of Chowla's averages over arbitrary rectanglesProduct and Quotient Set Dominance in Finite GroupsOn Quadric Surfaces Weighted by Arbitrary CoefficientsHecke Eigenform Product Identities for Full-Level Hilbert Modular FormsThe order types of the supports of $p$-adic algebraic Hahn seriesStieltjes constants for Hurwitz-type L-series attached to periodic arithmetic functionsTowards linear growth for biprojective hypersurfaces of small dimensionReal Fiducial Vectors Only Exist in Dimensions $d\equiv 3 \pmod{4}$On the Quantitative Bounds of Nonlinear Roth TheoremHecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$Short Recurrences and Straight-Line Programs for PrimesSharp Bounds for Limits of $N$-Point CorrelationAppell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-FunctionsRegularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of $(-1)^{\omega(n)}$On a conjecture on Romanoff type representationsOn Divisor Function Polynomials and Dirichlet SeriesOn the saturability of $p$-adic Lie groupsAn Infinite Family of Ap\'ery-like Recurrences for Euler's ConstantCovering plane curves over finite fields with linesKhintchine dichotomy for images of self-similar measures and almost random walksHigher mod $p$ Satake transforms: explicit formulas and images for $\mathrm{GL}_2$Thurston's Legacy at the Interface of Surface Dynamics, Train Tracks, and ArithmeticCampana strong approximation on generalised Markoff surfacesWeighted, GIT and N\'eron--Tate heights on genus-two moduli and JacobiansCounting with Hiccup SequencesThe Tate Conjecture for Ordinary Calabi-Yau Threefolds

arXiv math.NTの新着論文52本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-09/ The Integer Values of $\sum_{i=1}^{n}\frac{1}{\gcd(n,i)}$The structure of irreducible cuspidal eta quotientsLogarithmic moments of the Rogers Ramanujan continued fraction and odd zeta valuesMultiplicity Constants for Rough Numbers in Prime GapsFinite-radius Jensen and relative-entropy formulations of the Balazard--Saias--Yor criterionSimple and accurate approximations to Dirichlet $L$-functionsA Generalization of the Riemann Functional Equation with Three VariablesIrreducibility of Generalised Laguerre Polynomials for Large Integer ParametersClassification of the Orbits of Three Quadratic Collatz-type MapsSimultaneous non-vanishing of twists of $\mathrm{GL}_3$ and $\mathrm{GL}_1$ $L$-functionsLong intervals of consecutive composite values of polynomialsCardinalities of Jordan Diophantine sets of upper triangular integer matricesNon-degeneracy and Fibering with Applications to Diophantine ApproximationEquidistribution of number theoretic point sets in the torus and the sphere in Wasserstein metric and $L^2$ discrepancySplitting fields of complex hyperbolic groups: matrix extraction, Hermitian descent, and spectral fieldsAdditive Sums of Generalized Shifted Ternary Divisor FunctionsA note on Riemann's $R$-function and almost primesA combinatorial proof of the quadratic Gauss sumHorizontal moments of Kloosterman sums and a density version of sievesAutomorphic symbols and automorphic \emph{L}-values of GL(2) over imaginary quadratic fieldsStatistics of divisor functions over function fieldsRay class monoids for orders of number fieldsWeak and genuine A_n-formality for number fieldsInvariant Measures on Smooth Algebraic Groups over Higher Local FieldsDiscorrelation of the M\"obius function with linear phases in short intervalsNew Hoffman-type generators for alternating multiple zeta valuesA Unified Framework for $p$-adic Congruences and $p$-adic Interpolations of Sequences$q$-Supercongruences Modulo the Third and Fifth Powers of a Cyclotomic Polynomial$q$-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruencesUniform Height Gaps in Arbitrary CharacteristicsPythagorean pairs in boxes of prime powersUniform non-vanishing of prime quadratic twists of standard and symmetric square $L$-functionsUnipotent Selmer dimensions for CM curves via Iwasawa lociFurther bounds in the polynomial Szemer\'edi theoremHyperplane winning for bad in manifoldsA uniform bound for the minimal degree of an isogeny between principally polarized superspecial abelian surfacesGeometric families of multiple elliptic Gamma functions and arithmetic applications, IIIOn $a^4+b^4+c^4+d^4=(a+27(b+c+d))^4$ and ten other new infinite familiesOn Igusa's conjectures for weighted homogeneous polynomials with isolated singularitiesSlightly improved zero-free half-planes for the quasi-Riemann hypothesisTwo Primes and Five Mixed Fibonacci-Lucas SummandsGeometrically Abelian Sections on Higher-Dimensional VarietiesThe Erd\H{o}s-Falconer distance problem in the integer latticeK-Moduli Wall Crossing and Automorphic Forms for the Moduli Space of Rational Elliptic SurfacesK-moduli wall crossing for quasimaps to a projective varietyContinuity of the Julia sets in non-archimedean and hybrid settingsOn the asymptotic behavior of the number variance of random points on the unit torusArithmetic Progressions in Midpoint ColouringsLargeness of the wild locusRational curves on toroidal compactifications of Picard modular varietiesA Complete Proof of Mueller--Ho ConjectureTwisted Jacquet modules and induction from Speh representations

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 PrimesConsecutive Cycle SumsMore than 83.9% of the zeros of the Riemann zeta function are distinct and more than 67.35% are simple and on the critical lineAutomorphisms of general modular curvesAffine Coordinate Subspaces and Strong Khintchine ConvergenceIdempotence in Carmichael and Giuga numbers and its application to the Agoh-Giuga conjectureOn a Digital Signature Based on Matrix Decomposition and the MinRank ProblemOn 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 PappasHigher order uniformity of the primes and cancellation of the M\"obius function in shorter intervalsPrime points on smooth hypersurfacesLinear independence of values of polylogarithms with periodic coefficients, outside the disk of convergenceMaximal volume of convex bodies avoiding random points and lacunary dilatesTranslation-invariant equations in $\mathbb{F}_p^n$ and groupsTerminal Blocks of Primes in Pisot Numeration SystemsSpacing statistics for a point scatterer on the cubic three-torusConsecutive Rankin-Cohen Bases, Full-Spark Periods, and Divisor-Tau CongruencesInvariant Primes in Lubin-Tate Space and Hovey-Strickland at Every HeightGenerating sets for maximal orders in rational quaternion algebrasImproved average and almost-all bounds for $G(n)$Irrationality exponents of logarithms of positive rational numbersIntersecting a curve in an abelian variety with multiples of another curveLocal Factors in the BSD Conjecture: A Unified Statistical ViewCocycle Relations and Elliptic Gamma ValuesMixed moments of arithmetic functions and Kloosterman sums$p$-class groups in the cyclotomic $\mathbb{Z}_p$-extension of imaginary quadratic fieldsEquivariant Unirationality of Cubic ThreefoldsMaking 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

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/2026-10-07/ Densities of Picard Rank Jumps for K3 Surfaces Over Global FieldsCUDA-MPQS: A GPU-Resident Self-Initializing Quadratic Sieve, and the Factorization of RSA-155On the class number of real multiquadratic fieldsThe One-Power Erd\H{o}s Conjecture for Primes $p \equiv 7 \pmod{36}$Systems of equations with elements of finitely generated groups and with linear recurrence sequencesOn eutactic formsLifting ethereal Bianchi modular formsGaps theorems for linear forms with cubic coefficientsFurther results on the paramodular Hecke algebraPrimitive normal progressions in finite fieldsA new bound for the Furstenberg--S\'ark\"ozy theorem using the van der Corput propertyCarlet's cyclic-additive conjecture for the Kasami monomialsA concise proof of the 8 case of Sylvester's conjectureThe Artin-Davenport conjecture on cubic formsThe average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integerPerfect powers with few digits and $S$-unit coefficientsPrimitive Fourier Coefficients of Hermitian Klingen-Eisenstein SeriesAlgebraic Eisenstein classes for $\mathrm{GL}_n$ with applications to the Bianchi caseGenerating and generalizing MSTD sets through Markov processesOn S\'{a}rk\"{o}zy's Local Extrema ConjecturesThe least prime with a given primitive root and a variant of the larger sieveLocal newforms, Pa\v{s}k\={u}nas-Stevens Whittaker functions, and explicit test vectors for $\mathrm{GL}(n)\times \mathrm{GL}(n)$New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutationsNew algebraic points on covers of elliptic curvesMixing of the BCZ MapHigher additive energies on discrete cubesBlock decompositions in the p-adic Langlands correspondenceSemisimplicity, purity and Mumford-Tate conjecture for hyper-K\"ahler varietiesSpecial Loci in the Moduli of CurvesOn the structure of certain valued fields IIRandom Cayley sum hypergraphs and $k$-fold sumsets

arXiv math.NTの新着論文55本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-06/ The Riemann-Siegel remainder as a fractional summandGaps, isolated points, and the origin of the ray in the one-dimensional Dirichlet spectrumExponential generating functions for Apostol-Dedekind and related sumsNonvanishing of special $L$-values of cusp forms on $\mathrm{GL}(2)$ with totally split prime power twists: without the class number hypothesisOn Mahler $U$-numbers under rational mapsOptimal large sieve for fixed order charactersMoments and Large Geometric Monodromy for Linearly Constrained Kloosterman FamiliesSequential exponential-motivic periods in spatially cut-off $\phi^4_2$Iterated cotangent-difference integrals over totally real cyclotomic fieldsPrescribed ideal classes and elliptic points in Ennola cubic fieldsCubic Progressions on Smooth Plane CurvesNote on fractional sum of the divisor functionFew small primes suffice to cover unit groupsBorwein-Bradley-type identities for Ramanujan-type series for $1/\pi^4$Supercongruences for Domb numbersProofs of some OEIS conjectures on Wythoff sums, Fibonacci and Lucas wordsThrough the lens of the Eisenstein idealError Term Estimates for Sets of RemaindersDyadic Structure of the Two-Block Odd Partition Function and Theta-Weighted Congruences for $pod(n)$An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebrasOn the generalized Sierpi\'nski and Riesel numbersOne-level density of zeros of the Riemann zeta function weighted by its special valuesThe main conjecture for a Vinogradov subsystemSharp mean value estimates in the absence of translation-dilation invarianceFour-square polynomial triples: quadratic classification and equal-degree obstructionsOn the factorization of $x^{d_{r}} + x^{d_{r-1}} + \cdots + x^{d_{2}} + x^{d_{1}} + p$ and a conjecture of C. NicolAb-faithfulness of absolute Galois groups in number theorySlope Stability for ${\mathbf Z}_p$-Towers of CurvesAmicable numbersAn Algebraic Proof of the Non-Modularity of Solutions to the Canonical Modular Differential EquationIdeal-Smooth Sets and an Explicit Upper Bound for the Real Sum-Product ExponentAutomorphic commutator relations in relative geometric LanglandsConflict-avoiding codes and near-primitive rootsA proper arithmetic surface with infinite \'etale fundamental groupWhen the BSD Real Period Remembers Elliptic Curves over $\mathbb{Q}$A Variant of the Fractional Gamma-regularized Zeta KernelTower of coverings and polylog-size coverings of rational pointsTheta Series with Half-integral CharacteristicsA Bogomolov property for moduli spaces of polynomials over abelian extensionsHow close can rational points get to a manifold?Counting zero-sum subspaces for the multiplicative inverse functionGolod--Shafarevich for arithmetic surfacesChowla Conjecture for the truncated M\"obius function over $\mathbb{F}_q[t]$Degeneracy loci and unlikely intersections in abelian schemes$7$-adic Galois representations of elliptic curves over the rationals via Kummer descentThe linear independence of $1$, $\zeta(3)$, and $\zeta(4)$ETM-3D: A One-Parameter Multistable Quadratic Flow with an Explicit Absorbing Set and Intermittent ChaosInfinite log-concavity of the Taylor coefficients of the Riemann xi-functionUniform positivity of the tau invariantWeak approximation for Campana points on projective spacesTempered Symplectic Distinction For Quaternionic $GL_n(D)$: A Conjecture of PRASADOn three conjectures of Kimberling concerning the array $\lfloor k\varphi^n\rfloor$Polynomials with restricted support and maximal zeros on a finite Cartesian setGeneric Hodge and special Hodge--Witt polygonsSpreading out perverse sheaves

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/2026-10-05/ Arithmetic growth in partially commutative semigroups of endomorphismsThe proportion of polynomials over F_2 with positive orthogonal multiplicityShimura Reciprocity for Real Quadratic FieldsCounterexamples for Rational Points Near CurvesThe Prime Wavelet Tree: Compressing the Carmichael NumbersExtreme values of Dirichlet $L$-functions on the critical line with a growing prime modulusA uniform degree bound for modular rank-two Nahm sumsThe Wang--Sun Sum over Affine DerangementsA new upper bound for the irrationality exponent of $\zeta(2)$some arithmetical aspects of the two dimensional jacobian conjectureTelescopic Structure of Numerical Semigroups Generated by Unsigned Stirling Numbers of the First KindCohomology of Linearly Constrained Kloosterman Families: Newton Polytopes, Weights, and Boundary MonodromyCubic arithmetic-geometric mean and isogenies of Hesse elliptic curvesSplit-Cubic Curves from D(n)-Triples: A Bounded Finite-Field CensusPellarin's Identity, Carlitz Period, and Anderson Generating Functions over Arbitrary CurvesThe quality plane of $abc$-triples and the decomposition into gainsGosper's and Ramanujan's infinite products and generalizationsA cubic Chabauty criterion for hyperelliptic curvesEisenstein congruences in tame families and the class group of a metabelian extensionSum-product patterns in the shifted primesHausdorff dimension for exactly approximable matricesExplicit second moments of symplectic Siegel transformsQuantitative Gowers uniformity of the primes in intervals of length $X^{5/8+\varepsilon}$Exact diameter compression for four-point sumset cardinalitiesPappas's conjecture on ramified unitary local modelsResolving Erd\H{o}s-Ulam Monochromatic Union-Closed Family ConjecturesSharp rational points counting near nondegenerate curves in $\mathbb{R}^n$Sturmian beta-shifts do not have typical periodic optimization

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