Counting Points over Finite Fields and Hypergeometric Functions
Number Theory
2012-01-17 v1
Abstract
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 . 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.
Cite
@article{arxiv.1201.3335,
title = {Counting Points over Finite Fields and Hypergeometric Functions},
author = {Adriana Salerno},
journal= {arXiv preprint arXiv:1201.3335},
year = {2012}
}