Gaussian hypergeometric series and supercongruences

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Title: Gaussian hypergeometric series and supercongruences
Authors: Osburn, Robert
Schneider, Carsten
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Date: 2009
Online since: 2016-09-15T16:05:33Z
Abstract: Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the number of Fp points on algebraic varieties and to Fourier coefficients of modular forms. In this paper, we explicitly determine these functions modulo higher powers of p and discuss an application to supercongruences. This application uses two non-trivial generalized Harmonic sum identities discovered using the computer summation package Sigma. We illustrate the usage of Sigma in the discovery and proof of these two identities.
Type of material: Journal Article
Publisher: American Mathematical Society
Journal: Mathematics of Computation
Volume: 78
Start page: 275
End page: 292
Copyright (published version): 2008 American Mathematical Society
Keywords: CongruencesSymbolic computation
DOI: 10.1090/S0025-5718-08-02118-2
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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