Extending Gaussian hypergeometric series to the $p$-adic setting
Number Theory
2012-10-09 v1
Abstract
We define a function which extends Gaussian hypergeometric series to the -adic setting. This new function allows results involving Gaussian hypergeometric series to be extended to a wider class of primes. We demonstrate this by providing various congruences between the function and truncated classical hypergeometric series. These congruences provide a framework for proving the supercongruence conjectures of Rodriguez-Villegas.
Keywords
Cite
@article{arxiv.1204.1574,
title = {Extending Gaussian hypergeometric series to the $p$-adic setting},
author = {Dermot McCarthy},
journal= {arXiv preprint arXiv:1204.1574},
year = {2012}
}
Comments
Int. J. Number Theory, accepted for publication