Hasse invariants and mod $p$ solutions of $A$-hypergeometric systems

Abstract

Igusa noted that the Hasse invariant of the Legendre family of elliptic curves over a finite field of odd characteristic is a solution mod $p$ of a Gaussian hypergeometric equation. We show that any family of exponential sums over a finite field has a Hasse invariant which is a sum of products of mod $p$ solutions of $A$-hypergeometric systems.

22 pages

References in corpus (1)

• Congruences for L-functions of additive exponential sums

Cited by in corpus (1)

• Exponential sums and finite field $A$-hypergeometric functions