Hypergeometric type identities in the $p$-adic setting and modular forms
Number Theory
2014-07-25 v1
Abstract
We prove hypergeometric type identities for a function defined in terms of quotients of the -adic gamma function. We use these identities to prove a supercongruence conjecture of Rodriguez-Villegas between a truncated hypergeometric series and the Fourier coefficients of certain weight four modular form.
Cite
@article{arxiv.1407.6670,
title = {Hypergeometric type identities in the $p$-adic setting and modular forms},
author = {Jenny G. Fuselier and Dermot McCarthy},
journal= {arXiv preprint arXiv:1407.6670},
year = {2014}
}