Hypergeometric functions over finite fields satisfy a classical-style symmetry, proven by constructing isomorphisms between algebraic varieties whose rational point counts equal the functions.
A Lauricella hypergeometric series over finite fields
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In this paper we introduce a finite field analogue of a Lauricella hypergeometric series. An integral formula for the Lauricella hypergeometric series and its finite field analogue are deduced. Transformation and reduction formulae and several generating functions for the Lauricella hypergeometric series over finite fields are obtained. Some of these generalize certain results of Li \emph{et al} and Greene as well as several other known results.
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Symmetry of hypergeometric functions over finite fields and geometric interpretation
Hypergeometric functions over finite fields satisfy a classical-style symmetry, proven by constructing isomorphisms between algebraic varieties whose rational point counts equal the functions.