Overcolored Partition Restricted by Parity of the Parts
This paper extends the recently defined function , which counts multicolored partitions with specific color restrictions for even and odd parts, to the context of overpartitions.
🔢 Category
math.NT
178 papers
A Comparison of Gauge Dimension and Effective Dimension
This paper characterizes the gauge profiles of sets of reals defined by effective dimension and demonstrates a separation between these sets and -well approximable numbers using Hausdorff measure.
Classifying integer tilings and hypertilings
This paper classifies all tame integer tilings and hypertilings by developing a geometric model based on generalised Farey graphs in the hyperbolic plane, which connects these structures to triangulated polygons, friezes, and the Cayley hyperdeterminant.
Arithmetic dynamics and Generalized Fermat's conjecture
This paper proposes a generalized Fermat's conjecture within the framework of arithmetic dynamics, provides supporting evidence for it, and introduces a multi-indexed version of the conjecture.
Diophantine approximation with mixed powers of Piatetski-Shapiro primes
This paper proves that for any real and constants satisfying necessary conditions, there exist infinitely many triples of Piatetski-Shapiro primes satisfying a specific linear Diophantine inequality with mixed powers, provided the exponent is sufficiently close to 1.
Explicit conditional bounds for the residue of a Dedekind zeta-function at
This paper establishes new, concrete, and explicitly numerical conditional bounds for the residue at of the Dedekind zeta-function associated with a number field.
Infinite linear patterns in sets of positive density
This paper characterizes all possible infinite linear configurations that exist within the shift of any set of positive upper Banach density, thereby unifying and generalizing Szemerédi's theorem on arithmetic progressions and the recent density finite sums theorem.
Desingularization of double covers of regular surfaces
This paper provides explicit equations describing Lipman's desingularization for double covers of regular surfaces, thereby establishing a concrete algorithm to resolve their singularities.
On Ruzsa's conjecture on congruence preserving functions
This paper proves that Ruzsa's conjecture on congruence-preserving sequences holds true if the associated generating function has at most two singular directions at the origin, thereby showing that any potential counterexample must exhibit at least three such directions.
The Second Moment of Sums of Hecke Eigenvalues I
This paper computes the first and second moments of sums of Hecke eigenvalues for holomorphic cusp forms averaged over large weights, revealing distinct size transitions at and within the regime where the sum length is smaller than .
Witt Group of Nondyadic Curves
This paper computes the derived Witt groups of smooth proper curves over nondyadic local fields of characteristic not equal to 2 by utilizing reduction techniques and conducting a general study of the existence of Theta characteristics.
Analytic Properties of an Orthogonal Fourier-Jacobi Dirichlet Series
This paper establishes the meromorphic continuation and, in the specific case of the lattice, a precise functional equation for a Dirichlet series involving Fourier-Jacobi coefficients of cusp forms on orthogonal groups of signature by utilizing an integral representation derived from Klingen-type orthogonal Eisenstein series and their connections to Epstein and Siegel Eisenstein series.
Theta Operator Equals Fontaine Operator on Modular Curves
Inspired by Pan's work, this paper provides a new proof that an overconvergent modular eigenform of weight $1+kp$, achieved by demonstrating that the theta operator coincides with the Fontaine operator.
Smooth polynomials with several prescribed coefficients
This paper investigates the distribution of -smooth polynomials over finite fields with prescribed coefficients by employing character sum estimates, adapting Bourgain's argument, and analyzing double character sums.
Functionality for isomorphism classes of curves and hypersurfaces
This paper presents algorithms grounded in invariant theory to address geometric problems concerning curves and hypersurfaces, with a primary focus on those of genus 2, 3, and 4, while also incorporating new theoretical results derived from the first author's PhD thesis.
The Hofstadter consecutive-sum sequence omits infinitely many positive integers
This paper resolves a conjecture from OEIS entry A005243 by proving that the greedy self-generating sequence defined by Hofstadter, where each term is the smallest integer greater than the previous one representable as a sum of at least two consecutive earlier terms, omits infinitely many positive integers.
The SQInstructor: a guide to SQIsign and the Deuring Correspondence with level structures
This paper presents a generalized framework for the SQIsign signature scheme by incorporating level structures into the isogeny challenge, which leads to a new explicit Deuring correspondence for supersingular elliptic curves and solutions to constrained norm equations.
Antisymmetry of real quadratic singular moduli
This paper confirms the Darmon-Vonk conjecture on the antisymmetry of real quadratic singular moduli by analyzing rigid meromorphic cocycles for the split orthogonal group on four variables and establishing the modularity of a generating series of Kudla-Millson divisors.
The unstable complex in Bruhat-Tits buildings for arithmetic groups over function fields
This paper establishes that for a principal congruence subgroup over a function field , the -unstable region of the Bruhat-Tits building for is homotopy equivalent to the spherical Tits building for , extending Grayson's generalization of Serre's earlier result for .
The Flint Hills Series, Mixed Tate Motives, and a Criterion for the Irrationality Measure of
This paper establishes that the convergence of the Flint Hills series is equivalent to the irrationality measure of being at most $5/2\zeta(3)L(3, \chi_{-3})$.