Counting Points over Finite Fields and Hypergeometric Functions

Details Counting Points over Finite Fields and Hypergeometric Functions Counting Points over Finite Fields and Hypergeometric Functions

2012-01-16

arxiv.org/abs/1201.3335v1

Mathematics

Number Theory

Scientific paper

It is a well known result that the number of points over a finite field on the Legendre family of elliptic curves can be written in terms of a hypergeometric function modulo $p$. In this paper, we extend this result, due to Igusa, to a family of monomial deformations of a diagonal hypersurface. We find explicit relationships between the number of points and generalized hypergeometric functions as well as their finite field analogues.

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