Supercongruences for Apery-like numbers

Abstract

It is known that the numbers which occur in Apery's proof of the irrationality of zeta(2) have many interesting congruence properties while the associated generating function satisfies a second order differential equation. We prove supercongruences for a generalization of numbers which arise in Beukers' and Zagier's study of integral solutions of Apery-like differential equations.

8 pages, revised version, to appear in Adv. in Appl. Math

References in corpus (1)

• Elliptic integral evaluations of Bessel moments

Cited by in corpus (9)

• Supercongruences for sporadic sequences
• Multivariate Apéry numbers and supercongruences of rational functions
• A supercongruence for generalized Domb numbers
• Some supercongruences on truncated ${}_3{F}_2$ hypergeometric series
• Proof of two conjectures of Z.-W. Sun on congruences for Franel numbers
• New representations for all sporadic Apéry-like sequences, with applications to congruences
• Sequences, modular forms and cellular integrals
• Congruences Among Power Series Coefficients of Modular Forms
• On sporadic sequences