Transformations of well-poised hypergeometric functions over finite fields

We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transformation and summation formulas. Some of these results are analogous to those given by Dixon, Kummer and Whipple for the we...

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Bibliographic Details
Published in:Finite fields and their applications Vol. 18; no. 6; pp. 1133 - 1147
Main Author: McCarthy, Dermot
Format: Journal Article
Language:English
Published: Elsevier Inc 01.11.2012
Subjects:
Character sums
Gauss sums
Hypergeometric function over finite fields
Modular forms
Transformations of hypergeometric series
secondary
Modular forms
Hypergeometric function over finite fields
Gauss sums
Character sums
primary
Transformations of hypergeometric series
ISSN:1071-5797, 1090-2465
Online Access:Get full text
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Summary:We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transformation and summation formulas. Some of these results are analogous to those given by Dixon, Kummer and Whipple for the well-poised classical series. We also discuss this functionʼs relationship to other finite field analogues of the classical series, most notably those defined by Greene and Katz.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2012.08.007