Counting points over finite fields and hypergeometric functions

Adriana Salerno
2013 Functiones et Approximatio Commentarii Mathematici  
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. 2010 Mathematics Subject Classification. 11G25, 33C20, 14G05 .
more » ... ey words and phrases. counting rational points over a finite field, hypergeometric functions.
doi:10.7169/facm/2013.49.1.9 fatcat:bijpwdrh2jaspid5j24tfhod5y