1243 papers
This paper constructs combinatorial multiple Eisenstein series, a family of -series that interpolate between a given rational solution of the extended double shuffle equations and multiple zeta values, serving as -analogues closely related to modular forms and defined via symmetril and swap invariant bimoulds.
This paper unifies order-3 -formulas and Apery-like kernels within a rank-2 Conservative Matrix Field framework by proving they arise as shifted lifts of explicit order-2 kernels derived from Gauss-square coefficients and Domb numbers, while establishing a functoriality that classifies these structures and generates 11 new integer sequences via Belyi pullbacks.
This paper investigates the equation and demonstrates that, under the assumption of the explicit abc conjecture, the equation admits only finitely many nontrivial solutions in certain special cases.
This paper presents a complete formalization of the Ramanujan–Nagell theorem in Lean 4, detailing the proof strategy, architectural design, and challenges involved in verifying the theorem's integer solutions through the computation of algebraic number theory concepts such as the ring of integers, class number, and unit group of .
This paper determines the order of magnitude of the -th moments of the sum of a random multiplicative function twisted by the Fourier coefficients of a fixed modular form for the range .
This paper derives exact formulas for the number of non-negative integer solutions to the linear Diophantine equation $ax+by+cz=n$ when the coefficients are three consecutive Fibonacci or Lucas numbers, thereby resolving previously unsolved summations of floor functions found in Binner's earlier reciprocity-based approach.
This paper utilizes a specific sesquilinear form to realize the small theta lift for even orthogonal-symplectic and unitary dual pairs over p-adic fields.
This paper establishes natural identifications between the Brauer-Manin sets of a smooth quasi-projective variety over a finite extension and its Weil restriction , specifically when has a trivial abelianized fundamental group or when is projective with a torsion-free geometric Picard group.
This paper establishes that almost free Banach -vector spaces over a complete valuation field are free under assumptions of -strong compactness or weak compactness of their cardinality, serving as non-Archimedean analogues of classical results for almost free Abelian groups.
This paper establishes upper and lower bounds for the Chevalley-Bass number of fields of characteristic zero, provides an algorithm to compute this value given the maximal abelian subextension, and applies these results to improve a constant in exponential Diophantine equations.
This paper establishes a conditional, -independent upper bound on the number of cuspidal isobaric summands in the symmetric -th power lift of a cuspidal automorphic representation for , assuming specific Langlands functoriality conjectures and extending the analysis to cases with relaxed cuspidality conditions.
This paper establishes the existence and uniqueness of an inhomogeneous Beatty sequence with slope as a second monotone solution to the order-2 almost Golomb equation, characterizing its validity across a continuous family of parameters and verifying the identity for various window sizes while noting its failure for even perfect squares.
This paper demonstrates that for certain rank 1 finite groups of Lie type, the conductor of any complex irreducible character is realized at a single group element, thereby providing a specific instance of a potential strengthening of W. Feit's conjecture through methods combining algebraic number theory and character tables.
This paper establishes the existence of an explicit constant beyond which no regular ternary sum of generalized -gonal numbers exists for any integer .
This paper investigates the unique sharpness of the Cohn-Elkies linear programming bound for sphere packing in dimensions 8 and 24 by analyzing three independent necessary conditions from number theory, lattice theory, and conformal field theory, ultimately proposing a conjecture that these conditions are equivalent for dimensions divisible by 8 and unified through the Bost-Connes quantum statistical system.
This paper constructs and establishes the equivalence between three distinct D-module models for the minimal representation of the conformal group of an even-dimensional quadratic space, while also providing a geometric proof of the finite generation of the associated differential operator algebra and introducing a quadric Fourier transform.
This paper presents an algorithm for computing the Pyasetskii involution on local Langlands parameters for the classical groups , , and by combining Moeglin-Waldspurger's method for with Lanard-Mínguez's approach for Aubert-Zelevinsky involutions, while also providing a geometric interpretation for the bad parity case.
This paper improves the exponent in the local -norm estimate for the error term of the hyperbolic circle problem for the modular group, conditionally on a twisted Linnik-Selberg-type conjecture regarding sums of Salié sums.
This paper establishes an equivalence between the homotopy category of Hovey's Gorenstein projective model structure on pro- Iwahori-Hecke modules for semisimple rank one groups and the singularity category of an explicit scheme, thereby recovering Grosse-Klönne's mod- Langlands correspondence for and providing a complete explicit description for and .
This paper establishes a structural upper bound on the -adic valuation of denominators for rationals in missing-digit sets, providing an effective finiteness criterion for reciprocals of various sequences (such as superfactorials and Fibonacci products) that generalizes and extends recent results on reciprocals of factorials.