Some mixed character sum identities of Katz II

Ron Evans; John Greene

doi:10.1007/s40993-016-0071-5

Some mixed character sum identities of Katz II

Ron Evans, John Greene

Mathematics & Statistics

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Abstract

A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p> 3. His proof required deep algebro-geometric techniques, and he expressed interest in finding a more straightforward direct proof. The first author recently gave such a proof of his identities when q≡1(mod4), and this paper provides such a proof for the remaining case q≡3(mod4). Our proofs are valid for all characteristics p> 2. Along the way we prove some elegant new character sum identities.

Original language	English (US)
Article number	8
Journal	Research in Number Theory
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s40993-016-0071-5
State	Published - Dec 1 2017

Bibliographical note

Publisher Copyright:
© 2017, The Author(s).

Keywords

Eisenstein sums
Gauss and Jacobi sums
Hasse–Davenport theorems
Hypergeometric F character sums over finite fields
Norm-restricted Gauss and Jacobi sums
Quantum physics

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Some mixed character sum identities of Katz II

Abstract

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