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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Vydáno v:	Finite fields and their applications Ročník 18; číslo 6; s. 1133 - 1147
Hlavní autor:	McCarthy, Dermot
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.11.2012
Témata:	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
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Popis
Shrnutí:	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