Extending Gaussian hypergeometric series to the p-adic setting

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Abstract

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.
Original languageEnglish
Pages (from-to)1581-1612
JournalInternational Journal of Number Theory
DOIs
StatePublished - Aug 27 2012

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