Hasse invariants and mod p solutions of A-hypergeometric systems

Alan Adolphson; Steven Sperber

doi:10.1016/j.jnt.2014.02.010

Hasse invariants and mod p solutions of A-hypergeometric systems

Alan Adolphson, Steven Sperber

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	183-210
Number of pages	28
Journal	Journal of Number Theory
Volume	142
DOIs	https://doi.org/10.1016/j.jnt.2014.02.010
State	Published - Sep 2014

Keywords

A-hypergeometric
Hasse invariant

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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.",

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AU - Sperber, Steven

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AB - 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.

KW - A-hypergeometric

KW - Hasse invariant

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JO - Journal of Number Theory

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Hasse invariants and mod p solutions of A-hypergeometric systems

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Keywords

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