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 $p$. 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.
Citation
Adriana Salerno. "Counting points over finite fields and hypergeometric functions." Funct. Approx. Comment. Math. 49 (1) 137 - 157, September 2013. https://doi.org/10.7169/facm/2013.49.1.9
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