Congruences via modular forms

Abstract

We prove two congruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide a table of congruences for numbers which appear in similar power series expansions and in the study of integral solutions of Apery-like differential equations.

8 pages, revised version, to appear in Proceedings of the AMS

References in corpus (1)

• Supercongruences satisfied by coefficients of 2F1 hypergeometric series

Cited by in corpus (7)

• A supercongruence for generalized Domb numbers
• New representations for all sporadic Apéry-like sequences, with applications to congruences
• Sequences, modular forms and cellular integrals
• Modular forms, hypergeometric functions and congruences
• Congruences Among Power Series Coefficients of Modular Forms
• On sporadic sequences
• Congruences for the Almkvist-Zudilin numbers