プレプリどんどん: math.NT

arXiv math.NTの新着論文32本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-16/Atoms in the Semigroup of Non-Negative Integer MatricesPower and rank-weighted sums in dense finite Sidon setsRational 2-Cycles for $x^3+bx+a$ and the Elliptic Family $Y^2=X^3+4X^2+16t^2$Every natural number is a sum of distinct semiprime unit fractionsOn concatenations of two $k$-generalized Pell numbersCounting Algebraic Integers of Bounded Height in Cyclotomic FieldsA full $p^{4r}$ supercongruence tower for a level-three symmetric-cube hypergeometric sequenceLarge values of quadratic Dirichlet $L$-functions of prime-related moduliThe Bateman-Horn conjecture on average for generalized von Mangoldt FunctionsA Beyond Endoscopy Derivation of the Functional Equation for the Symmetric-Square L-FunctionSquare-root cancellation for sums of coefficients of $\operatorname{GL}(m)$-automorphic forms over values of random polynomialsA parametric family of primes p = km(m+1) + e + 2kq: heuristic laws, conditional theorems, and unconditional primality certificatesOn periodic sign changes for weighted representations of integers as colored sums of triangular and generalized pentagonal numbersThakur's hypotheses on power sums of $\mathbb{F}_q[t]$Indivisibility of ray class groups of real quadratic fieldsTwo $q$-congruences from Jackson's ${}_8\phi_7$ summation and Andrews' ${}_4\phi_3$ summationThe difference of the sums of odd and even parts of restricted partitionsObstructions and kernel transport for Hecke lifts of partition q-bracketsDivided differences and complex variations of multiple zeta-star valuesGeneralized Bell polynomial operators arising from generalized normal orderingQuantitative Oppenheim Conjecture for Random Quadratic Forms and Optimal Variance Bounds in Function FieldsA counterexample to the near-quadratic Elekes--R\'onyai expander conjecture over $\mathbb R$Footnote to a theorem of Phagan on actions of a cyclic groupOn the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygonsTransformers Learn the Mestre-Nagao HeuristicThe distribution of the de Moivre experimentDominant Zeros of Nekrasov--Okounkov PolynomialsDual Affine Spiral Orbits on $\mathbb{Z}^2$ Generated by Paired Unit SquaresNon-Archimedean balanced metrics and their application to totally degenerate abelian varietiesTorsors of Generalized del Pezzo Tori and Brauer GroupsAn Asymmetric Formula for Interval Consonance and its Relation to Harmonic CoincidenceThe Grothendieck-Katz Conjecture for privileged local systems

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/2026-06-15/On $U_p$-congruences for meromorphic modular forms with supersingularitySecondary terms for first moments of Selmer groups of twists of elliptic curves over global function fieldsResidue Restrictions for a Two-Color Partition SeriesAlmost perfect inhomogeneous powers in arithmetic progressionCounting the number of $1_{n}$-preperiodic integral points of a discrete dynamical system with applications from arithmetic statistics, VIIA Weil Sum Approach to Permutation Polynomials over Quadratic Extensions of Finite FieldsSum of parts in overpartitions and partitions without repeated odd partsSemistable reduction of smooth quarticsExplicit local stable resolution of cuspsValidated numerics for the Gauss problem on continued fractionsAdelic line bundles over a N\'eron model

arXiv math.NTの新着論文12本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-12/Lower bounds on expressions depending on the functions {\boldmath$\varphi(n)$}, {\boldmath$\psi(n)$} and {\boldmath$\sigma(n)$}, IIIRoot Clusters and Multiclusters over Imperfect Hilbertian FieldsAn AI Proof of 18-Variable Undecidability for Diophantine Equations over $\mathbb Z[i]$Splitting of Polynomial Families via Galois TheoryEffective Estimates for a Class of Farey Fraction Sums and Bounds for Mundici-Type ConstantsMulti-target hyperbolic sieves and elliptic trace obstructionsRamanujan's and Lim's Identities and Harmonic Maass--Jacobi FormsDiscrete Fourier Transform Approach to Cyclically Covering Subspaces of $\mathbb{F}^n_q$Some new modular Nahm sums of ranks 3 and 4Split primes and the Elekes-R\'onyai problemTrace spectra of simplices in large setsSphere Packings in Higher Dimension (after Boaz Klartag)

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/2026-06-11/Rankin--Selberg Subconvexity via Spectral ReciprocityMultivariate Period RingsThe p-adic Cauchy Theorem and Overconvergent Period SheavesProofs of two $q$-congruence conjectures of GuoModular variants of p-adic fundamental sequenceCapparelli's partition theorem as part of an infinite hierarchy: Combinatorial and Weighted Words extensions of recent workA note on a conjecture of NgAnswer to a decomposition question on tori raised by Colliot-Th\'el\`ene and SansucBeating Product Constructions for Linear Equations Over Finite FieldsOn Perfectoidizaiton of Finite Algebras over a Perfectoid RingModuli of Supersingular Abelian Varieties in Dimensions $g\leq 5$

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/2026-06-10/On partial T-adic exponential sums and partial exponential sums with p-power conductorA generic categorical local Langlands correspondence for quasi-split reductive groupsA Tsang-range high-moment bound for $\operatorname{Im}\log L(\tfrac12+it,\chi)$ under GRHPrime Quadruplets and Jump Conditions on Arithmetic FunctionsUnique decomposition of ordersOn the Ekedahl sieve for the singular locus of the discriminant polynomialHilbert irreducibility for algebraic pointsEisenstein-Kronecker classes on Hilbert moduli spaces and a new construction of Katz's $p$-adic measureLinear relations of four conjugates of an algebraic number of degree eightA Divisor Parametrization for the Erd\H{o}s--Straus ConjectureWeighted partitions with interval restrictions: exact formulas and a bivariate master identityAdjacent comparison bounds and extremal sets for Ruzsa numbersA natural e\~ne product construction of the Big Witt ringMaximal Transcendentality of the Double-Scaled PCMInd-Banach approach to Grothendieck duality in Rigid-analytic geometryOn superspecial hyperelliptic curves of Rosenhain formsThe convergent stackOn the rank of hypergeometric sheaves on higher dimensional tori

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/2026-06-09/Arithmetic Symmetry in Ideal Prouhet-Tarry-Escott SolutionsExplicit bounds for Dickman's functionWeighted Recursions for the Smallest Parts FunctionMinkowski shapes of pure number fieldsOn the sequence $\mathrm{gcd}(a^n-1,b^n-1)$Monogenity of Fibonacci polynomials and Lucas polynomialsA criterion for weighted uniform distribution along functions from a Hardy fieldGcd-closed sets and divisibility among power LCM matrices$P$-adic $L$-functions: $t$-modules and Dirichlet-Goss $L$-seriesWaring's problem involving D.H. Lehmer numbersArithmetic exceptionality of generalized Chebyshev polynomials of the second kindErd\H{o}s Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian FluctuationsMurmurations in the Depth Aspect for Maass and Modular FormsOn special perfect polynomials over $\mathbb{F}_2$Uncertainty Principles for the Number Theoretic TransformA convexity proof of Pohst's inequalityOn the degree-$2$ Siegel theta series of extremal even unimodular lattices of ranks $48$, $72$, $96$, and $120$Extremal Type II lattices of rank $72$ are generated by their second shellTranscendence of simple geodesics on finite modular coversZeta functions over curvesThe Dirichlet spectrum with respect to $L_1$ norm is $\left[\frac12,1\right]$Polynomial Corners Over finite FieldsDegenerate generalized Stirling operators of the first kind arising from generalized Heisenberg algebraWeil's quadratic form via the screw functionFourier Coefficients of Siegel--Eisenstein Series of Degree $2m$ and Weight $m+1$Insufficiency of the algebraic Brauer--Manin obstruction for homogeneous spacesAbelian surfaces of small conductor from genus 3 double coversMultiple zeta values ending with a fixed stringOn the Smallest Counterexample to the Log-Concavity of the D'Arcais PolynomialsFine-scale statistics for $\mathbb{Q}^n$Power Integral Bases in Polynomial CompositionsA note on large values of Dirichlet $L$-functions for characters of fixed order at $1/2On the Vinberg Family of K3 SurfacesCovering $\mathbb{F}_2^n$ with Hamming BallsBirkhoff genericity on affine subspaces in horospheresDigit Mixing under Polynomial MapsRestriction estimates for toral eigenfunctions and lattice points in spherical regionsAlgebraic Hodge generic points are denseBertini theorems for Hilbert-Samuel multiplicity over finite fields

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/2026-06-08/Vanishing Coefficients in Products of Quintuple ProductsTamagawa number formula for JacobiansA mod $p$ determinant criterion for Cohen--Lenstra convergence of random $p$-adic matrices with prescribed zero patternsNote on the Equivalence of Costas Polynomials and OrthomorphismsMulti-scale properties of continued fraction setsConnection between the Riemann zeta-function and random matrices via hyperfunctionsOn the factorizations of integers via division algorithms for polynomialsTwisted Moments of Rankin-Selberg $L$-functions in the Prime-Power Level AspectExact output statistics of Icart's encoding in the exceptional \(j=0\) caseGaps in Multiplicative Sidon Sets IIErd\H{o}s-Kac theorems for discriminants of number fieldsOn the Absolute Geometry of $\operatorname{Spec}\mathbf{Z}$On periods and Jacobians of Heisenberg curves

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/2026-06-05/Corrigendum to "Isomorphism classes of Drinfeld modules over finite fields"Theorem $(1+1.9)$ on the Goldbach ConjectureThe Case of the Second Smallest Modulus: or why we cannot be arbitrarily careless?Hasse-Weil Zeta Functions Modulo a PrimeOn explicit Fourier expansions of theta lifts to ${\rm SO}(3,n+1)$ arising from elliptic newforms of level oneExotic and inverted Kloosterman sums over semisimple algebrasDrinfeld modules in rank 2 with CM and S-unit j-invariantsArithmetic Wu Formulas and the Generalized Hecke TheoremRecent Progress around Cohen-Lenstra HeuristicsAn Elementary Analysis of the Prime Partition FunctionA Generalization of the Amdeberhan-Andrews-Ballantine ConjectureOn a conjecture on Romanoff type sumsetsNo three algebraic conjugates of degree sixteen sum to zeroArithmetic statistics of isogeny Selmer groups associated to hyperelliptic curvesArithmetic Kashiwara Regularity and Orbit Classification for Filtered Strongly Equivariant $\mathcal{D}^{\dagger}$-ModulesHiggs bundles on the Fargues-Fontaine curveTwo notes on valued fieldsDecomposition Theorem for Perfectoid Rings along General IdealsStability of the smooth Casselman-Jacquet functor

arXiv math.NTの新着論文14本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-04/Enumeration of modular forms for $\Gamma_1(N)$Voronoi-Hankel TransformsWeighted Recursions for Hurwitz Class NumbersDigit frequencies and class numbersAn Explicit Surjectivity Threshold for Digit Sums of PrimesRepresentations of positive integers by three almost-prime squaresCorrespondence of discrete series representations of $\mathrm{GSp}_{2n}$ and its inner formInteger points close to a transcendental curve: an algorithmic approachThe leading constant in Malle's conjectureKhintchine's Theorem for Symmetric matrices via Flows on the Space of Symplectic LatticesA Note on Jacobians with Prescribed FactorsPrimitive inhomogeneous approximation for fixed non-singular frequenciesLocal-global conjugacy questions for affine extensionsStochastically evolving ellipsoids with symmetries

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/2026-06-03/A Note on Diophantine Approximation with Restricted DenominatorsA Fibonacci theorem for Collatz trajectories via modular graph structureGeneralized polygonal number representationsExplicit generators of the space of modular formsOn the Schematic and Analytic Constructions of the Local Langlands CategoryOn the Argument of the Lerch, Chowla--Selberg Formula and CM Values of $\eta(\tau)$Diagonal Condition in Multiplication Table of $\displaystyle {\, \mathbb{Z} [i] / (\alpha) }$Planes in quadratic 4-space and associated shapes of latticesMajorization and Gaussian-Mass Maximality for Construction-A Lattices from Binary Self-Dual CodesThe Fontaine operator at cusps of modular curves at infinite levelPair correlation of $\alpha n^{\theta}$ for random $\theta$A $q$-Analogue of a Supercongruence Related to Van Hamme's (B.2) SupercongruenceSome new results on determinants and permanentsA note on partitions in the image of pre$_2$On maximal Dynkin friezesA conjecture of Glasby, Praeger, and Unger on permutations of $S_n$On $\mathbb J$-strata with Parahoric Stabilizers in Affine Deligne-Lusztig VarietiesCassini's identity for k-bonacci numbersAn Iwasawa-type asymptotic formula for multiple $\mathbb{Z}_p$-coverings of graphsOn the prime field spherical restriction conjecture in four dimensions: breaking the Stein-Tomas exponent and applicationsComplete Families of Curves in the Moduli Space of Genus g CurvesHalf of finite abelian groups are unit groupsThe Abel--Jacobi map over the twistor-$\mathbb{P}^1$ and real local class field theory

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/2026-06-02/Perfect powers in the product of denominators of elliptic curvesOn $\mathbb{Z}_2$-extensions of real quadratic fieldsPrescribed realisation of longest runs in continued fractionsPolylogarithmic Analogues of Euler's ConstantOn the $P(t)$-adic Littlewood conjecture in odd characteristicsLocating a shortest vector in certain $2$-dimensional latticesOn indecomposable elements in latticesThe categorical local Langlands conjectureA further study of polynomial $g_{n,q}$ over finite fieldsTopological and Diophantine properties of lattice subset projectionsTame Galois Groups, Linking Numbers and MildnessPiatetski-Shapiro Primes in short intervalsAdditive Rigidity for Images of Rational Points on Abelian Varieties II: The General CaseA Sharp Reverse Minkowski Inequality for the Gaussian Mass of Integral Unimodular Lattices Through Rank $32$Sums of Apostol's M\"{o}bius functions of order $k$Distinguished defining polynomials for extensions of p-adic fieldsGeometrization of summation formulae for quadricsHigh moments of random multiplicative functions twisted by Fourier coefficients of modular formsIntrinsic Subgroups and the $\ell$-adic Galois imageOn a problem on a generalization of Euler's totient functionOn cyclotomic matrices related to Kloosterman sums over finite fieldsInfinite Moments of Class Groups for Solvable Fields with a Normal Abelian SubgroupApplications of a formula of Maesaka-Seki-Watanabe type for multiple harmonic $q$-sumsUniversality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columnsOn the unit equation $\varepsilon+\delta=n$ in cubic fieldsOn periods of Elliptic curvesArithmetic regularity as an alternative to transferenceCyclotomic factors of rational necklace functionsAnalogues of the Lindel\"of Hypothesis for the Barnes multiple zeta function and related problemsFinding the complement of an elliptic curve inside a JacobianThe Primes are $2$-AccessibleInfinitely many holes in connectedness loci for collinear affine iterated function systemsNon-Archimedean Massera-Schaffer-Maligranda-Pecaric-Rajic InequalityHitting Arithmetic Progressions at the Square-Root ScaleThe 1/2-Conjecture for $q$-Binomial Coefficients with Fractional IndexThree-color van der Waerden numbers grow super-exponentially

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/2026-06-01/Density of subsets of squarefree elements in certain Dedekind domainsOn the density of rational lines on diagonal cubic hypersurfaces, IITranscendence and measures via the refined Diophantine exponentAn Improvement of Konstantoulas' Density ConstantPerfect powers among Jacobsthal numbersIntegrality of Averages of Roots of Unity and Perfect IsometriesThe Bogomolov property for $p$-supercuspidal eigenformsVisible 2-torsion in the Tate-Shafarevich group of an elliptic curveOn the asymptotic average diameter of blocks of uniformly distributed sequences and related resultsMoments of partition statistics, Bell polynomials and Eisenstein-type series

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/2026-05-29/On Ramanujan's $q$-Continued Fractions of Order Thirty-Four and Sixty-EightAsymptotic formulas for sums of elements from a multiplicative groupOn a conjecture of GoldmakherMersenne numbers and the doubling mapWeierstrass semigroups at totally ramified places of degree one on linearized function fieldsOn the power of the discriminant of a univariate polynomial as a certain determinant in positive characteristicInducing Whittaker Functions from Higher RanksThe weighted large sieve through ParsevalIwasawa invariants of Bertolini--Darmon Theta ElementsCanonical extensions of $p$-adic shtukas on toroidal compactifications of Shimura varietiesBourgain's $L^2$ pointwise ergodic theorem over function fieldsSubsequence Sums in PermutationsSuperspecial plane quintics with large automorphism groupsLift-independence problem in the $P$-adic Simpson correspondence for curvesA note on Azumaya algebras and one-forms

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/2026-05-28/Some Remarks on $\tau$-Congruent NumbersLinnik's problem for multiplicative functions$Q$-difference analogue of the Stothers-Mason theoremGood Integers: (T,k)-Subclasses and Applications to Galois Duality in Coding TheoryMixed thresholds in the Lonely Runner ConjectureTransformation Formulae and Applications for Double Lambert SeriesAdditive Diophantine Equations involving S-Units, Factorials and Ternary Recurrences with repeated rootMetrical theory of signed Engel expansionsA unified proof of conjectures on the spaces of multiple $q$-zeta valuesOn the analytic continuation of the Riemann zeta functionEquidistribution of CM points and RM curvesThe sum-product conjecture is false for real numbersRiemann and the logarithmic derivatives of zetaProofs of Two Positivity Conjectures of GuoBrauer--Manin obstruction from failure of Kodaira vanishing in positive characteristic

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/2026-05-27/A note on uniform version of Littlewood inequality and Fibonacci numbersOn planar functions over $\mathbb{F}_{q^3}$Problems in additive number theory, VII: The structure of additive $h$-bases for $n$Connected components of the ranges of twisted divisor functions on number fieldsNotes on congruence zeta functions via a Berkovich approachTowards a generalized Maeda conjecture for modular forms with quadratic nebentypusSaturation and No-Go Theorems for Scalar Poisson Certificates of Gaussian Mass MaximalityLower bounds for the Hausdorff dimension of expressible setsUltra Kolyvagin systems and higher Fitting ideals of Iwasawa Selmer groupsWords for generalized Markov numbersProducts involving the real parts of Jacobi sums and related cyclotomic matricesEkedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varietiesThe Northcott Property for Composites of Number Fields of Bounded DegreeInhomogeneous Approximation by Sums of RootsThe V/L recursion for Macdonald's 7th Variation Schur polynomialsPrime Certificates for Exact Vertex-Coprime Ramsey NumbersRank-two recurrence results for polynomials and questions of dynamical Mordell--Lang typeA Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\mathbb{R}^4$Structural properties and tilting correspondences of perfectoid towers

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/2026-05-26/On some arithmetic conditions of recurrent sequences modulo prime pOn the Harris-Viehmann conjecture for Hodge-Newton reducible local Shimura data of abelian typeOn the binary digits of the Erd\H{o}s-Borwein constantThe $\theta = \infty$ Conjecture and the Riemann Hypothesis for Automorphic $L$-functionsCounting Rational Points on Danielewski and Double Danielewski Surfaces over Finite FieldsTribonacci properties of identities, matrices, and determinantsValuation Separation for Coprime Lucas ProductsEquality in a Reverse Minkowski Shell Bound for Integral Lattices via Spherical DesignsSimultaneous Periods for Families of Rational Maps Modulo PrimesHilbert-90 quotient maps, torsion defects, and symmetric monodromyLubin-Tate representations over nontrivial finite Galois extensions of $\mathbb{Q}_{p}$ are not Aut-intrinsically Hodge-TateVariational estimate for the family of discrete averages associated to simplicesThe Frobenius problem for shifted square sequences starting with a multiple of 4A Note on Abelian Monogenic TrinomialsIncidence Obstructions for Power Products in Elliptic Divisibility SequencesBanded quadratic digit functions along irreducible polynomials over finite fieldsA proof of the $4,7$ cases of Sylvester's conjecture on cube sumsBoundary CM points and class groups of small exponentOrbit decomposition statistics for discrete dynamical systems: the Ces\`aro mean and a large deviation principleOn the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve $Y^{q+1} = X^n(X^n + 1)$The $\Delta$ property: a bridge between split graphs and Number TheoryLattice point counting problems on step-two nilpotent Lie groups

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/2026-05-25/The Poisson Tail Conjecture for Primes in Short IntervalsCullen and Woodall numbers in Padovan and Perrin sequencesDistributions of Iwasawa $\lambda$-invariants of $\mathbf{Z}_p$-towers over supersingular isogeny graphsOn modular forms of rational weight satisfying the canonical second-order linear modular differential equationCongruence Classes of Supporting the Erd\"{o}s-Straus Conjecture I: Tame SolutionsComputing Gamma(p/q) with Beta function valuesConcise and elegant proofs of three formulas for complete Bell polynomialsSets of large values of polynomial multi-correlation functionsDefinability via the tilting correspondenceTop-dimensional rational cohomology of the congruence subgroup $\Gamma_{0,n}^+(p)$Balanced intersection size distributions in projective planes

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/2026-05-22/On the Natural Density of Monic Integer Polynomials with Roots in a Fixed Number FieldPort Fillings for Primary Pseudoperfect NumbersA generalization of the Erd\H{o}s-Sierpi\'nski conjectureA Matrix-Theoretic Exact Formula for Counting Primes in Intervals Between Consecutive Odd Squares2007: An Arboreal Odyssey: A View of Arboreal Galois Representations and Applications, from Early in the Subject's HistoryEscaping Chaos in Random Multiplicative FunctionsRational dynamics of a prime-representing mapThe reverse Goldbach problem and a refined Zsiflaw--Legeis theoremCoset-refined trace statistics, nodal characters, and affine branches in cubic norm toriA Uniform Random-Lattice Tail Bound for the SVP Kissing-Profile ParameterOn the structure of fine Mordell-Weil groups over a $\mathbb{Z}_p$-extension and its intermediate subextensionsThe distribution of semi-integral points on a class of singular cubic hypersurfacesA quick distributional way to reproduce some results of the Riemann zeta functionA Complete Characterization of Heron Triangles with Two Perfect Square Sides and the All-Square Equivalence ConditionArboreal Galois Groups of a PCF Map with Strictly Pre-periodic Critical PointsRethinking the work of Langlands on Eisenstein seriesLines in the prime number graphBell Transforms of Arithmetic Functions: Euler Products, Congruences, and Polynomial SequencesBases of associated Galois modules in general wildly ramified extensions and in elementary abelian extensions of degree $p^2$From Hilbert's Tenth Problem to Quantum Speedup: Explicit Oracles for Bounded Diophantine SystemsGraphs from quadratic forms and vector spaces over finite fieldsClosed geodesics in short intervals for random hyperbolic surfaces

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/2026-05-21/High-Precision Approximation of Riemann Zeros via the Truncated Weil FormEigenvalue Distribution of $p$-adic Random Matrices Among Algebraic Extensions, with an Analogue for $p$-adic Random PolynomialsBounded-box reductions in the Subbarao-Warren problem for unitary perfect numbersOn discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generatorLimiting Distribution and Rate of Convergence for GL(3) Fourier CoefficientsBeyond endoscopy for $\mathsf{GL}_2$ over $\mathbb{Q}$ with ramification 4: contribution of non-elliptic partsGeneralized Fermat equation over cyclotomic $\mathbb{Z}_l$-extensions of totally real fieldsPrecise Asymptotics and Exact Formulas for Tensor Product Energies of Fibonacci LatticesA Local Valuation Criterion for Quadratic-Permutation Interleaved Zadoff--Chu SequencesQuasiautomorphic forms are isomorphic to vector-valued automorphic formsOn a conjecture of Amdeberhan, Andrews and Ballantine for double Lambert seriesBinomial coefficients with divisors avoiding an intervalAn Improved Upper Bound for the Dirichlet Spectrum in Diophantine ApproximationArithmetic Properties of Overcolored Odd PartitionsSharp omega results for the divisor and circle problemsManin's conjecture for semi-integral curves and $\mathbb A^1$-connectednessMeasuring Decidability as Related to Busy Beaver NumbersExtensionalism without Logicism: Ambrose and Extensional LogicAn explicit lower bound for the unit distance problemThe pro-\'etale fundamental group of singular schemesRemarks on the disproof of the unit distance conjectureA strange continued fraction associated with the Romik map

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/2026-05-20/The generalized Montgomery-Hooley formula: A surveyShort Salem polynomialsFibonacci Numbers and Vieta Jumping for a Rational Diophantine EquationHal\'asz theorems for Gaussian ideals in sectors and short intervalsOn nonconvex constellations among primes II: (458,3240)A formula of counting divisors in integers rings: a generalization of the divisor function $d_0(n)$On optimal $p$-adic uniformization of unitary Shimura curvesA Determinant Congruence Conjectured by SunSun-type determinant and permanent congruencesTwo determinant evaluations in Sun's conjectures involving Legendre symbolsOn the Goldbach problem with restricted primesThe inhomogeneous Khintchine Theorem in dimension twoSplit-prime supercongruence at the mixed CM point (1/6, 1/3; 1)A Fourier-Free Density-Increment Proof of Roth's TheoremMotivic Galois theory for one-loop Feynman integrals in momentum space

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/2026-05-19/Boundary Value Problems on $p$-Adic Analytic ManifoldsFactorization of Additive Polynomials and van der Geer--van der Vlugt curves in characteristic 2Explicit Formulas for the Casimir Eigenvalues of $SL(n,\mathbb{Z})$-Maass FormsOne-level densities of large even and odd orthogonal families of automorphic L-functionsGaps of Binary Numerical Semigroups and of Binary Inclusion-Exclusion PolynomialsCounterexamples to integer-coefficient criteria for recurrence along functions from a Hardy fieldA Degree-Two Hilbert--P\'olya Realisation by Causal Riemann-Surface OperatorsOn the finite transcendence of Frobenius traces for abelian varieties over $\mathbb{Q}$Multiplicative independence in the sequence of $k$-generalized Pell numbersLinear independence of periods related to polylogarithmsAn update on the Linnik--Goldbach and Romanov problemsNon-admissibility of some universal supersingular representationsA note on the $q$-adic valuation of $\sigma_k(n)$Decay of weighted cusp counts for congruence subgroups of $SL_2$ over number fieldsOn some constancy of Hecke eigensystems for Drinfeld cuspforms of level $\Gamma_1(\mathfrak{n}\wp^r)$On the Periods of Ikeda-Yamana Lift for the Unitary Group ISum of consecutive powers as a perfect powerClassicality of Hilbert modular formsThree Brillhart-Lehmer-Selfridge primality proofs for Wagstaff numbersCovering systems where the prime divisors of all moduli are only $2$, $3$, or $5$Linear equations in Piatetski-Shapiro primesEpstein vector zeta functions related to the ADE Lie algebrasn-ary elliptic groups, rings, and primes in arithmetic progressionsModule Lattice Security (Part III): Structured CVP Distance on the Log-Unit LatticeRationality problem for norm one tori of tensor products of \'etale algebras and Hasse norm principleExplicit cost analysis of Toom-4 multiplication for incomplete NTT in lattice-based cryptographyIterative maps emerging from cohomological structure of primesGenus formulas for dormant modular curves and asymptotic behavior of their function fields

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/2026-05-18/Improvements to Jacobian Arithmetic in Global Function FieldsCounting solutions to the quadratic determinant equationExplicitly combing hedgehogs over fields of Stufe 4On the Face Map of the Admissible Set With Iwahori LevelBailey pairs, Eichler integrals and unified Witten-Reshetikhin-Turaev invariantsPositive density for Sun's $2^k+m$ conjectureEisenstein circle packings and the Eisenpint Schmidt arrangementDuality of analytic Hopf algebras and the Amice transformHecke Eigenvalues of Ikeda LiftsOn Drinfeld's representability theoremExtensions of the Furstenberg-S\'ark\"ozy theorem via the arithmetic level-$d$ inequalityA Weyl-type theorem for Diophantine approximations driven by LCA groups and applicationsLocal newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: ReductionA new construction of permutation polynomials over $\mathbb{F}_{q^3}$On the number of directions formed by Cartesian products in $\mathbb{F}_{p^2}^2$Evaluation of two determinants involving $q$-integers

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/2026-05-15/A Generalized Closed Form of Ramanujan-Type Fourier Cosine Transform via Meijer's G-FunctionParity vectors and paradoxical sequences in the accelerated Collatz mapLocal certification of residual squareclasses in $\mathbb Q(\sqrt{2},\sqrt{pq},\sqrt{ps})$: one-bit, affine, and finite-choice Hilbert-symbol frameworksPresentations of Galois groups of unramified extensions of global fields and its predicted distributionKodaira-Neron statistics for rational elliptic curves with $j$-invariant 0 and 1728How Twist Class Redundancy Drives the Prediction of Traces of Frobenius of Elliptic CurvesL-indistinguishability for covering groups of algebraic toriFibonomial determinantsA density version of quaternary Goldbach problemOn Maximal Prime GapsPatterns on elliptic curves beyond Bremner's conjectureOn Vu's restricted box estimate in Waring's problemSolutions for Hecke Sum Questions of Banerjee and BringmannReal geometric transcendence for the Gamma functionConstruction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP CodesMcShane-Rivin norm balls and simple-length multiplicitiesSophie Germain, math\'ematicienne extraordinaire: A story stranger than fictionThe R\'enyi entropy of the order of a random permutationImproved Ramsey bounds for generalized Schur equations

arXiv math.NTの新着論文12本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-14/A connection between low-lying zeros and central values of $L$-functionsComponentwise height bounds for polynomial value-set liftingWieferich Primes and Monogenic TrinomialsOn Galois Embedding Problems Arising from 3-Torsion of Elliptic CurvesLarge values of shifted mixed character sumsFields where torsion forms decomposeTautological modular forms of level two and degree twoAlmost Affine Invariance Over Prime Fields: Green Problem 90Nonexistence of certain classes of generalized bent functions: Revisiting the element partition methodA note on arithmetic progressions with restricted differencesWhen Does the Dice Sum Become Prime?Graphs of Hecke operators in mixed ramification

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/2026-05-13/The 2-part of the Bloch-Kato conjecture, and indivisibility results, for $K_2$ of some elliptic curvesTwo dimensional arithmetic progressions avoiding squaresExplicit determination of a class of permutation rational functions in any characteristicBigness of Canonical Quadratic Points on Curves of Genus 4Weil-Moore animaSquared edge lengths of regular simplices with rational verticesHomological sieve and Manin's conjectureAnalytic Properties of Necklace PolynomialsLocal height arguments toward the dynamical Mordell-Lang conjecture$\ell^{p}$ improving estimates for multilinear forms motivated by distance graphs

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/2026-05-12/Frequency Ordered Ratio Families Arising from the Factorization of $p_{m-1}+1$A Complete Answer to Erd\H{o}s Problem 690Rational Base Descent: A Deterministic Algorithm for Factoring Structured SemiprimesSome Omega results for Dirichlet $L$-functionsMultiple integral representations of the Catalan's constantNon-$R$-trivial proper projective similitudes in type $A_3\equiv D_3$On the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_2$-extension of a family of real quadratic fields in which $2$ splitsRational points on smooth surfaces in $\mathbb{P}^3$ over finite fieldsOn the coefficients of the Taylor expansion of $L$-functions of elliptic curvesLow-Lying Zeros on the Critical Line for Families of Dirichlet $L$-FunctionsOn the exponent of distribution for convolutions of $\operatorname{GL}(2)$ coefficients to smooth moduliAn analogue of a formula of Popov IIThe variation of zeros of the Miller basisLacunary recurrences and 2-adic properties of Eisenstein seriesOn Ramanujan Primes for Hecke-Maass Cusp FormsCongruences of first syntomic cohomology groupsThe Serre Derivatives and Zeros of Modular FormsAn explicit Galois descent for multiple $t$-values of maximal heightProof of a conjecture of Andrews and Bachraoui on a Hecke sumReciprocals of Subsum Polynomials$p$-adic Congruencens of Generalized Euler Numbers and Relations to Even Zeta ValueLearning from Ramanujan: Elementary Approaches to Profound IdeasThe martingale evolution of probability measures defined via the sum-of-digits functionsInvariant measure for double base expansionsRefined obstructions to local-global principles for 0-cyclesDeterministically finding an element of large order in $\mathbb{Z}_N^*$Convergence of orbital integrals on unitary groups in positive characteristicPoisson approximation of random latticesA solution to a strengthened conjecture of Bukh, van Hintum and Keevash on additive bases

arXiv math.NTの新着論文12本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-11/Three-term arithmetic progressions of consecutive powerful numbersOn almost primes solutions to forms of odd degrees in many variablesPoissonian correlations of $\alpha n^d$ mod $1$Anderson generating function of rank-one Drinfeld Module over rational function fieldsA Deterministic Cryptographic Prime Generation Chain over Monogenic Cubic Number Fields and their GeneralizationsWeighted Distributions of Complex Multiplication Orders in Ordinary Isogeny ClassesRemarks on the distribution of Dirichlet $L$-functions along cosetsA strengthening of Chang's lemmaMultifractal analysis of power means for the Schneider map on $p\mathbb{Z}_p$On the refined local Langlands conjecture for discrete $L$-parameters of inner forms of quasi-split disconnected real reductive groupsBrik's sequence: a strange recursionOn ratios of theta functions

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/2026-05-08/A Structure Sheaf for Kirch TopologyMultiple modular L-functions and modular iterated integralsRankin--Selberg coefficients in arithmetic progressions modulo prime powersThe quotient problem for linear recurrence sequencesEvaluation of eight different families of cubic Euler sums$\delta$-Badly approximable numbers and ubiquitously losing setsA multidimensional Szemer\'{e}di theorem in integersOn algebraic twists with composite moduli, IIAsymptotic Statistics of Odd Unimodal Sequences: Rank Distributions and Probabilistic StructuresEquidistribution of Eigenfunctions of Quantum Cat Maps

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/2026-05-07/A new perspective on the rank of Mazur's Eisenstein Hecke algebraSpecial periods and some non-tempered cases of the Gan-Gross-Prasad conjectureRational orbits under correspondencesThin subbases of Piatetski-Shapiro sequencesFixed-point lifting and ghost periodic points for Chebyshev polynomials modulo odd prime powersA Ceiling Continued Fraction Approach to the Erd\H{o}s-Straus Conjecture: Heuristic finiteness of counterexamplesSmall values of signed harmonic sums and logarithmic means of multiplicative functions$\mathbb{G}_m$-cohomology of $p$-adic Stein spacesStatistics of the Genus Number of $S_3 \times C_2$ and $D_4$-fieldsExponential sums over singular binary quinticsNon-Expansive Matrix Based number SystemsMultiplicative $f$-ic forms on algebraic varieties arising from Thaine's generalized Jacobi sumsThe Logarithmic Asymptotic Phenomenon for Generalized Markov-Hurwitz EquationsThe top cohomology of principal congruence subgroups of special linear groups over Euclidean number ringsTheta functions and transformations of bilateral basic hypergeometric seriesAppell function proofs of recent and old mock theta function identitiesOn a polynomial involving quadratic residues modulo primesA Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics$p$-adic Manifold Learning and Benchmark Tasks from Impartial GamesThe McKay correspondence and local heights for wild-by-tame split metacyclic groupsEnergy and Vertex Energy of Modified Divisor Prime GraphsThe Erd\H{o}s-P\'osa property for prime-length cycles fails (and beyond)

arXiv math.NTの新着論文17本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-06/Sign changes of the Liouville function in arithmetic progressionsMonogenity of pure quintic fields: the power of sievingBehaviour of Certain Crystalline Representations modulo $2$Infinitesimal characters for the completed cohomology of $\mathrm{GL}_n$ over CM fieldsLectures on Condensed MathematicsOptimal embeddings for maximal orders of central simple algebras of degree 3 over number fieldsJoint extreme values of $L$-functions on and off the critical lineA multivariate Strassmann theoremCongruence rigidity of algebraic groupsReal approximation for homogeneous spaces with finite stabilizersOn the largest Sidon subset in a finite subset of $\mathbb{R}^N$Analytic summation of series involving higher-order derivatives of Chebyshev polynomials of the second kind and their applications to convolved linear recurrent sequencesTable-Based Encodings for Conway's Doomsday Algorithm: Vectorized Doomsdays and DoomyearsSigned sumsets and restricted signed sumsets in groups and fieldsCharacteristic-free approaches around Yu's constructionLectures on Analytic GeometrySmall Matrices with Small Inverses: Unimodular Zerofree Cases

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/2026-05-05/Monogenic Fields from Polynomial Compositions with ApplicationsSets of integers satisfying Bateman-Horn statisticsBowen--Franks groups and minus class groups of cyclotomic number fields with prime conductorA logarithmic structure theorem for multiplicative functions with small partial sums3-class field towers with 2 or 3 stagesA note on bilinear sums with modular square rootsArchimedean arithmetic Siegel--Weil formula for general weights over Shimura curvesNumbers in a Beatty sequence which are orders only of cyclic, abelian or nilpotent groupsOn the generalized inverse tangent integral and Catalan's constantGaps in Multiplicative Sidon SetsOn the Sum of a Prime and a Number that is not Square-FreeExpansion in $\text{SL}_2(\mathbb Z/q\mathbb Z)$ and Zaremba's conjectureCusp forms and parabolic cohomology classes for symmetric spaces of rank oneThe generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applicationsReductions of $\mathrm{GL}_2(\mathbb Q_{p^f})$-Banach spaces of slopes in $(0,1)$A bibasic double sum extension of a $q$-binomial theorem arising out of subspace enumerationFlat Cohomological Purity for Syntomic Schemes over Valuation RingsOn conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theoriesTwisting Higgs Modules and Functorial Aspects of the p-adic Simpson Correspondence

arXiv math.NTの新着論文14本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-04/The cardinality of a set containing the pairwise sums of a fixed number of integersPrimitive sets and von Mangoldt chains: Erd\H{o}s Problem #1196 and beyondEffective multi-equidistribution for translates of unipotent flows and Central limit theorems in inhomogeneous Diophantine approximationNotes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large PrimesExponent-one blockers and a Mordell-Weil construction of Euler bricksThe Hurwitz sum-of-squares problem depends on the base fieldModular Forms and Numerical Explorations of Rational Approximations to $\zeta(3)$On divisor sums due to Erd\H{o}s and RamanujanLang-Trotter phenomena and unlikely intersectionsA note on Zilber-Pink in $Y(1)^n$Conjectural duality for iterated $q$-integrals on $\mathbb{P}^{1}$ minus four generic pointsOn convex bodies with constant non-central sectionsDelta characters and crystalline cohomology of abelian schemesOn the largest sum-free subset of the lattice cube

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/2026-05-01/An $O_K$-basis for the image of a Lubin-Tate logarithm on $\pi$-regular extensions of $K$Mod p Monodromy of Cyclic Covers of the Projective LineSimple Lie Groups of type An as Galois groups over QOn the difference between perfect powers and integral $S$-unitsAn improved non-linear Roth-type theorem in finite fieldsA divisor function of Wigert and higher degree formsFrobenius Traces for Rank-2 Drinfeld Modules, Higher-Dimensional Galois Representations, and a Strong Multiplicity One Theorem in Positive CharacteristicA torsion-intersection proof of perfect-cuboid nonexistence on 1,072 explicit master-tuple fibersAsymptotic Vanishing of Stiefel--Whitney Classes for $\mathrm{GL}_n(\mathbb{F}_q)$Polynomial Maps with Constants on Matrix AlgebraThe proportion of permutations fixing a $k$-set

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/2026-04-30/Estimating the tail of the singular product in the multivariate Bateman-Horn conjectureCombinatorial sums derived from properties of Legendre polynomialsMonsky Matrix and 2-Selmer rankThe $p$-powers dividing certain exponential sumsSolution to the Erdos problem on distinct residues of factorialsFamilies of Unit Equations and Exponential Diophantine Problems via Integral PointsImproved bounds for the Fourier uniformity conjectureGeneralized Estermann problem for non-integer powers with almost proportional summandsOn the automorphisms of the power semigroups of a numerical semigroupMultiplicative convolution and double shuffle relationsOn Arithmetic Mirror Symmetry for smooth Fano fourfolds

arXiv math.NTの新着論文17本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-29/Elementary anabelian varieties are anabelianRamanujan, the taxicab problem for polynomials, and the abc-conjectureLinear recurrences and rational Lambert seriesTrilinear Kloosterman fractions I: partially fixed moduli and unbalanced convolutionsReciprocity and the Maslov PhaseCongruences via Partitions with Exactly Two Part SizesAdditive index and Carlitz rankThe Divisor Function along a Deterministic Orbit and the Emergence of LaddersThe threshold for linear independence of multiple zeta values in positive characteristicCyclotomic Numbers of Order $q-1$ over $\mathbb{F}_{q^r}$Some results on naive transcendence in the ring of integers modulo infinitely large primesConditional Upper Bounds for Large Deviations and Moments of the Riemann Zeta FunctionOn numerical semigroups with embedding dimension fourA structure theorem for sets with doubling $4+\delta$The local Langlands correspondence of essentially unipotent supercuspidal representations for disconnected reductive groupsA local-global correspondence for perfectoid purityMild Pro-$p$ Groups and Ordered Monoids

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/2026-04-28/Lattice point visibility along powers of polynomialsOn the integrality of modular functions over $\mathbb{Z}[j]$ and Kronecker-type congruencesA Proof of Bala's General-$m$ Representation of the Harmonic NumbersCore abaci and Diophantine equations I: fundamental weightHybrid Conjecture in a Mixed Shimura varietyDifferences of squares of upper-triangular $2\times 2$ integer matricesOn (not) learning the M\"obius functionA necessary condition for a congruent number of the form $8k+3$$2$-Selmer groups, $2$-class groups, and congruent numbersThe Absolute Anabelian Geometry of Virtual Curves of Arbitrary GenusPicking up the partial sums of the M\"{o}bius function problem with probabilistic number theoryLarge sieve inequality for sums of Legendre symbols over short intervalsUnbounded logarithmic limsup in Erd\H{o}s problem 684On optimization on ravine functions. Minkowski-Cohn moduli surface in Cohn parameterizationNon-Vanishing of Cubic Twists of $GL_n(\mathbb{Q})$ $L$-functionsOn the Gauss circle problem over smooth numbersOn D-cap-Modules of Finite Length on Rigid Analytic SpacesLinear Bounds for Differentiable Limits of Weak Pair Correlation FunctionsOn $k$-th power Diophantine triples of the form $\{a^k, b, c\}$Joint Sato-Tate Laws for Transformations of Hecke Eigenvalues: The Vertical CaseThe asymptotic oscillations of moments related to Dirichlet series with missing digitsOn the hull of linearized polynomial codesA Milestone in Formalization: The Sphere Packing Problem in Dimension 8A note on The asymptotic uniform distribution of subset sumsEleven, twelve, and thirteen lonely runnersDimension of the motivic Galois group of a 1-motiveA Necessary and Sufficient Condition for Uniqueness of Euclidean DivisionNewman's Tauberian theorem, the Riemann-Lebesgue Lemma, and abstract analytic number theoryOn classical doubling method gamma factors for certain depth zero representations

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/2026-04-27/A link between error terms when counting smooth and rough numbersThe exceptional set for Diophantine inequality with mixed powers of primesExceptional poles of archimedean Rankin-Selberg L-functions for principal series representations of GL(n,R)On a new modular equation of degree five and Eisenstein series identities of associated levelsHigher moments of the symmetric square $L$-function off the critical lineMatrices with cyclically monotone rows and Cantor numeration systemsKhintchine's theorem for inhomogeneous simultaneous approximation with polynomial decayAsymptotic behaviour of analytic torsion and cohomological torsion for $\mathbb{Q}$-rank $1$ arithmetic groupsNon-linear geometry of multiple zeta valuesNumerical Semigroups with $a_e = 2g+1$A construction method for WZ seeds

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/2026-04-24/On the reciprocity law in $\mathbb{F}_{q}[t]$Extremal Problems for GCDs and LCMs in Higher DimensionsRelations between higher level Hurwitz class numbersMoments and joint nonvanishing of symplectic $L$-functionsConsecutive non-square nom-primitive pairs in as finite fieldThe Smallest Invariant Factor of Elliptic Curves, and CoincidencesGalois representations over convergent de Rham period ringResidues of a tropical zeta function for convex domainsSpherical Cap $L_2$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap VariantLusztig constants and endoscopy

arXiv math.NTの新着論文12本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-23/Explicit density computations for certain sets of primes in Lucas sequencesOn Uniqueness of Mock Theta FunctionsMinimal $a$-numbers of Artin--Schreier covers of ordinary curvesRoot numbers for twisted Fermat quotient curves IIOn the $I(1)$-invariants: Non-abelian Hecke algebra caseOn the singularities of differential equations satisfied by $E$-functionsOn the Hyperbolic Fractional Sum of the Divisor FunctionNon-vanishing of the $p$-adic constant for mock modular forms associated to a newform with real Fourier coefficientsOn sums of two squares and a basis of order $2$p-adic elliptic polylogarithms and cubic ChabautyMellin transforms, transfinite diameter and rational approximations of integralsFractal transference principle for continued fractions of Laurent series

arXiv math.NTの新着論文14本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-22/Optimal Shifting Method in Dirichlet's divisor problemCharacterizing monogenic trinomials $\boldsymbol{x^{12}+ax^6+b}$ according to their Galois groupsAlgebraic numbers and Fourier analysis: Salem's third problemSums of Hecke eigenvalues along polynomial sequences and base change for $\text{GL}(2)$Classification of Rational Functions of Degree Three over Finite FieldsHandling some Diophantine equation via Euclidean algorithm and its application to purely exponential equationsBeyond the square-root barrier: cubic forms of Perazzo typeQuartic Rational Diophantine Quadruples and the Euler SurfaceDivision algorithms for norm-Euclidean imaginary quadratic fieldsRepresentations of binary quadratic forms by quaternary quadratic formsPseudometrics and preorders on sets of integer sequences induced by arithmetic functions functionsExplicit counting of ideals in number fields of arbitrary degreeGlobal Product Intersection Sets in SemigroupsIndependent Sets and Continued Fractions

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/2026-04-21/M\"obius disjointness conjecture for Furstenberg's flow on $\mathbb{T}^\omega$ in short intervalsReduction mod $p$ of semi-stable representations of some super-Breuil weightsGeometry-of-numbers methods over global fields II: Coregular representationsOn Regular Higher Power Rational Diophantine TriplesNon-liftability of Families of Abelian Varieties with Small $l$-adic Local SystemThe Limiting Distribution of Elliptic Dedekind SumsSupersingular Drinfeld modules, Brandt matrices, and rank-metric codesThe sum-product phenomenon for dense subsets of finite fieldsOn the normality of the concatenated Fibonacci constantMarkov fractions and Cohn matricesOrderings of Generalized k-Markov NumbersResolutions of spaces of crystalline representations and modularityEffective Joint Sato-Tate Distribution and Sign Change of Symmetric Power CoefficientsA remark on an integral structure of the imperfect coefficient ring of $(\varphi,\Gamma)$-modulesExplicit Kodaira-Spencer maps over PEL Shimura varietiesSemistable Reduction Theorem for Overconvergent $F$-isocrystals over Laurent Series FieldsDuality Between Prime Factors and The Prime Number Theorem For Arithmetic Progressions -- Higher Order DualitiesSophie Germain Primes and the Totient of Fibonacci NumbersSolvable Descent and the Grunwald Problem for Solvable GroupsA Rademacher exact type formula for pod$_2(n)$Families of symplectic Galois representations over small parabolic eigenvarieties for Siegel cuspforms of genus $2$A primality test for $Kp^\ell - 1$ numbersMaximal quadrics over finite fields and minimal codewords of projective Reed-Muller codesImplementing p-adic numbers in Macaulay2 using its foreign function interface and FLINTMarkov numbers of semigroupsElementary symmetric polynomials and a potentially injective family of maps on partitionsForbidden subgraphs in divisor graphs and an Erd\H{o}s divisibility problemSuperspecial generalized Howe curves of genus 4, 5, and 6 with completely decomposable JacobiansUnirational algebraic groups and tame ramificationNear-optimal density theorems for large dilates of large point configurations

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/2026-04-20/Non-standard Zeckendorf decompositions; or, Tribonacci within FibonacciGaussian Behavior and Geometric Gaps in Decompositions from Recurrences with Zero CoefficientsExtremal densities for forbidden configurations in $S$-smooth numbersBelyi map verification using certified path trackingUniform estimates for Delannoy numbers and dimension-free estimates for discrete maximal functions over cross-polytopesOn the surjectivity of $(T)$-adic Galois Representations of Drinfeld $A$-Modules of Rank 2 and 3: Density resultsOn a question of Astorg and Boc ThalerMatsuki duality for loop groupsSums of two symbols in $K_2(F)/2K_2(F)$ in characteristic twoAdolf Hurwitz and the Fundamental Theorem of Galois Theorie: The K\"onigsberg Lectures of 1890-1891

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/2026-04-17/The level-8 Apery-limit and a proof of the Ramanujan Machine conjecture Z1Arithmetic functions and learning theoryPrime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number TheoryOn the Number of Prime Factors of Consecutive IntegersComputer vision and converse theoremsAnother factor of integer polynomials with minimal integralsGelfand--Kirillov dimension and mod $p$ cohomology for inner forms of $\mathrm{GL}_2$Counting Theorems for Algebraic RelationsLog-Concavity and Infinite Log-Concavity of Linear Recurrent Sequences with Linear Coefficients via Companion Matrix MethodsRecurrence Time for Finite Quantum SystemsDistinguished Simple Supercuspidal Representations of $p$-adic $\text{GL}(n)$On local integrability results for $p$-adic reductive groupsEvaluations of some series via the WZ methodRational analytic syntomic cohomologyBorel--Bernstein and Hirst-type Theorems for Nearest-Integer Complex Continued Fractions over Euclidean Imaginary Quadratic Fields

arXiv math.NTの新着論文5本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-16/Representation of Ramanujan's tau function by twisted divisor functionsA proof of $p$-adic Gross--Zagier theorem via BDP formulaFourier Dimension in Duffin--Schaeffer ConjectureDistribution modulo one of linear recurrent sequences$p$-adic Linear Regression for Random Sampling with Digitwise Noise

arXiv math.NTの新着論文8本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-15/Simultaneous non-vanishing of Dirichlet L-functionsOn the $K$-extensions between Serre weights for unramified $\mathrm{GL}_3$The $p$-adic monodromy theorem over algebraic-affinoid algebrasMultivariable automatic arrays and transcendenceSolubility for families of norm equations coming from abelian number fieldsApplications of patching the coherent cohomology of modular curvesAn inverse theorem for sumsets of sets of positive density in the integersOn the number of missing integers in partitions

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/2026-04-14/Order-3 pi-formulas, Apery-like kernels, and Clausen functoriality for Conservative Matrix FieldsA comment on the equation $n!!=a_1!!\cdots a_t!!$A formal proof of the Ramanujan--Nagell theorem in Lean 4Low moments of random multiplicative functions twisted by Fourier coefficients of modular formsThe Number of Solutions to $ax+by+cz=n$ for Fibonacci and Lucas tripletsA note on small theta liftRemarks on Brauer-Manin obstruction for Weil restrictionsOn the Chevalley-Bass number of a fieldConjectural decomposition of symmetric powers of automorphic representations for $\mathrm{GL}(n)$Beatty solutions of almost Golomb equationsRegular ternary sums of generalized polygonal numbersLocal square mean in the hyperbolic circle problem and sums of Sali\'e sumsA Fixed-Prime Criterion for Reciprocals in Missing-Digit SetsBranched covers of $\mathbb{P}^1$ and divisibility in class groupThe solvability of the inverse volcano problem over non-prime finite fieldsAlmost Free Non-Archimedean Banach Spaces and Relation to Large CardinalsCharacter values and conductors of low-rank groups of Lie typeCusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24Geometrization of the Schr\"odinger Model for the Minimal Representation of an Even Orthogonal Group: The de Rham SettingAlgorithms on the Pyasetskii involution on local Langlands parameters of classical groupsPro-$p$ Iwahori-Hecke modules in semisimple rank one and singularity categoriesAn analogue of irreducible cuspidal representations for the group $PGL(2)$ over a two-dimensional local field

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/2026-04-13/Galois theory for finite fieldsSeven squares from three numbersDedekind zeta functions of non-Galois torsion fields of elliptic curvesA Dynamical Lifting Problem For Additive PolynomialsValues of algebraic functions at Liouville numbersIdentities and transformations for Lambert series and double Lambert seriesLinear recurrence sequences and palindromic concatenations of two repdigits in base $\beta$Differential operators on locally analytic Shimura varietiesQuartic reductions and elliptic obstructions for perfect Euler bricksBounding the exponential sum on squares of some sifted sequencesModular curves and bad reductionEffective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$A Neukirch-Uchida Theorem for 3-Manifolds

arXiv math.NTの新着論文8本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-10/On Lower Bounds for sums of Fourier Coefficients of Twist-Inequivalent NewformsUniversal sums of generalized polygonal numbers of almost prime lengthProofs for Andrews' Conjectures 5 and 6 on $v_1(q)$A Liouville-Type Inequality for Values of Mahler M-FunctionsResurgence of high-energy string amplitudesLifting banal representations of classical groupsL-modules are mixedOn a descent conjecture of Wittenberg

arXiv math.NTの新着論文20本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-09/On a perturbed Hofstadter $Q$-recursionOrder drop, Hecke descent, and a mod $p^4$ supercongruence for symmetric-cube hypergeometric coefficientsThe Domb Ap'ery-limit and a proof of the Ramanujan Machine conjecture Z2On the Double Lambert Series Conjecture of Andrews-Dixit--Schultz-YeeThe Thue-Morse TransformOn canonicity for integral models of Shimura varieties with hyperspecial levelReduced Unitary Whitehead Groups over Function Fields of p-adic CurvesBoundary Cohomology of Sp6(Z): Trivial RepresentationA Hal\'{a}sz-type asymptotic formula for logarithmic means and its consequencesArithmetic intersections on non-split Cartan modular curvesRandom conic bundle surfaces satisfy the Hasse principleExplicit inequalities for the nth lucky numberWeighted averages of arithmetic functions and applications to equidistributionOn the cohomology of negative Tate twists via cyclotomic descentOn a conjecture of Deines$p$-adic Theory for Partial Toric Exponential SumsCongruence modules and Wiles defects of determinantal rings of maximal minorsShort proofs in combinatorics, probability and number theory IITopological Indices of Divisor Prime GraphsA note on complex Lie Algebras isomorphic to their conjugate

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