Congruences via modular forms

Osburn, Robert; Sahu, Brundaban

doi:10.1090/S0002-9939-2010-10771-2

Congruences via modular forms
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by Robert Osburn and Brundaban Sahu PDF

Proc. Amer. Math. Soc. 139 (2011), 2375-2381 Request permission

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 tables of congruences for numbers which appear in similar power series expansions and in the study of integral solutions of Apéry-like differential equations.

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