Congruences via modular forms
Number Theory
2021-02-03 v2 Combinatorics
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.
Cite
@article{arxiv.0912.0173,
title = {Congruences via modular forms},
author = {Robert Osburn and Brundaban Sahu},
journal= {arXiv preprint arXiv:0912.0173},
year = {2021}
}
Comments
8 pages, revised version, to appear in Proceedings of the AMS