Appell-Lauricella hypergeometric functions over finite fields and algebraic varieties

Abstract

We prove finite field analogues of integral representations of Appell- Lauricella hypergeometric functions in many variables. We consider certain hypersurfaces having a group action and compute the numbers of rational points associated with characters of the group, which will be expressed in terms of Appell-Lauricella functions over finite fields.

arXiv comment26 pages