Modular forms, hypergeometric functions and congruences
Number Theory
2013-01-16 v1
Abstract
Using the theory of Stienstra and Beukers, we prove various elementary congruences for the numbers \sum \binom{2i_1}{i_1}^2\binom{2i_2}{i_2}^2...\binom{2i_k}{i_k}^2, where k,n \in N, and the summation is over the integers i_1, i_2, ...i_k >= 0 such that i_1+i_2+...+i_k=n. To obtain that, we study the arithmetic properties of Fourier coefficients of certain (weakly holomorphic) modular forms.
Cite
@article{arxiv.1301.3303,
title = {Modular forms, hypergeometric functions and congruences},
author = {Matija Kazalicki},
journal= {arXiv preprint arXiv:1301.3303},
year = {2013}
}
Comments
9 pages