Transformations of well-poised hypergeometric functions over finite fields. (English) Zbl 1276.11198
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 function’s relationship to other finite field analogues of the classical series, most notably those defined by Greene and Katz.
Keywords:
hypergeometric function over finite fields; transformations of hypergeometric series; Gauss sums; character sums; modular formsReferences:
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