Binomial coefficient-harmonic sum identities associated to supercongruences
Number Theory
2012-04-10 v1 Combinatorics
Abstract
We establish two binomial coefficient--generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of the author, they are used to establish modulo () congruences between truncated generalized hypergeometric series, and a function which extends Greene's hypergeometric function over finite fields to the -adic setting. A specialization of one of these congruences is used to prove an outstanding conjecture of Rodriguez-Villegas which relates a truncated generalized hypergeometric series to the -th Fourier coefficient of a particular modular form.
Cite
@article{arxiv.1204.1573,
title = {Binomial coefficient-harmonic sum identities associated to supercongruences},
author = {Dermot McCarthy},
journal= {arXiv preprint arXiv:1204.1573},
year = {2012}
}