Extending Gaussian hypergeometric series to the $p$-adic setting

Details Extending Gaussian hypergeometric series to the $p$-adic setting Extending Gaussian hypergeometric series to the $p$-adic setting

2012-04-06

arxiv.org/abs/1204.1574v1

Mathematics

Number Theory

Int. J. Number Theory, accepted for publication

Scientific paper

We define a function which extends Gaussian hypergeometric series to the $p$-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.

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