Another congruence for the Apéry numbers

DOI10.1016/0022-314X(87)90025-4zbMath0614.10011OpenAlexW2048654814MaRDI QIDQ1820190

Publication date: 1987

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-314x(87)90025-4

zbMATH Keywords

modular form Picard-Fuchs equation Apéry numbers congruence properties

Mathematics Subject Classification ID

Recurrences (11B37) (3)-folds (14J30) Congruences for modular and (p)-adic modular forms (11F33) Holomorphic modular forms of integral weight (11F11) Congruences; primitive roots; residue systems (11A07)

Related Items

Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs, The arithmetic and topology of differential equations, On some congruences involving Apéry-like numbers S_n, CONGRUENCES RELATED TO MODULAR FORMS, NEW CONGRUENCES FOR SUMS INVOLVING APÉRY NUMBERS OR CENTRAL DELANNOY NUMBERS, EXTENDING GAUSSIAN HYPERGEOMETRIC SERIES TO THE p-ADIC SETTING, Divisibility properties of sporadic Apéry-like numbers, Beukers-like supercongruences for generalized Apéry numbers, Some conjectural supercongruences related to Bernoulli and Euler numbers, Super congruences for two Apéry-like sequences, Proof of some conjectural congruences modulo p³, Supercongruences for truncated _{𝑛+1}𝐹_{𝑛} hypergeometric series with applications to certain weight three newforms, Super congruence for the Apéry numbers, A hypergeometric version of the modularity of rigid Calabi-Yau manifolds, Supercongruences on truncated hypergeometric series, Arithmetic properties of Apéry-like numbers, On congruences involving Apéry numbers, Dwork congruences and reflexive polytopes, Super congruences and Euler numbers, New Representations for all Sporadic Apéry-Like Sequences, With Applications to Congruences, Congruences of finite summations of the coefficients in certain generating functions, The asymptotic log-convexity of Apéry-like numbers, Supercongruences involving products of three binomial coefficients, Gessel-Lucas congruences for sporadic sequences, Proof of some conjectures of Z.-W. Sun on congruences for Apéry polynomials, Some supercongruences occurring in truncated hypergeometric series, A modular supercongruence for _6F_5: An Apéry-like story, On three conjectural congruences of Z.-H. Sun involving Apéry and Apéry-like numbers, On two congruences involving Apéry and Franel numbers, On sums of Apéry polynomials and related congruences, Modular forms, hypergeometric functions and congruences, ODD VALUES OF FOURIER COEFFICIENTS OF CERTAIN MODULAR FORMS, A $p$-adic supercongruence conjecture of van Hamme, Apéry polynomials and the multivariate saddle point method, The $L$-series of certain rigid Calabi-Yau threefolds, Supercongruences for polynomial analogs of the Apéry numbers, Two triple binomial sum supercongruences, Congruences for generalized Apéry numbers and Gaussian hypergeometric series, Apéry numbers, Jacobi sums, and special values of generalized $p$-adic hypergeometric functions, Values of Gaussian hypergeometric series, Supercongruences occurred to rigid hypergeometric type Calabi-Yau threefolds, Congruences via modular forms, Supercongruences for the Catalan-Larcombe-French numbers, Supercongruences for truncated hypergeometric series and p-adic gamma function, Supercongruences for sporadic sequences, On divisibility of sums of Apéry polynomials, Generalized Legendre polynomials and related supercongruences, Supercongruences involving Euler polynomials, Some $q$-analogues of supercongruences of Rodriguez-Villegas, Sequences, modular forms and cellular integrals, The 2-log-convexity of the Apéry Numbers, Automated discovery and proof of congruence theorems for partial sums of combinatorial sequences, Supercongruences for rigid hypergeometric Calabi-Yau threefolds, On a conjecture of Chowla et al, p-ADIC AND COMBINATORIAL PROPERTIES OF MODULAR FORM COEFFICIENTS, Congruences for sporadic sequences and modular forms for non-congruence subgroups, q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon, Holonomic relations for modular functions and forms: First guess, then prove, Two congruences concerning Apéry numbers conjectured by Z.-W. Sun, CONGRUENCES AMONG POWER SERIES COEFFICIENTS OF MODULAR FORMS, On two supercongruences involving Almkvist-Zudilin sequences, Supercongruences of Atkin and Swinnerton-Dyer type for Legendre polynomials, A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.

Cites Work