Some mixed character sum identities of Katz II

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 direc...

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Bibliographic Details
Published inResearch in number theory Vol. 3; no. 1; pp. 1 - 14
Main Authors Evans, Ron, Greene, John
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2017
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Number Theory
Quantum theory
Eisenstein sums
Gauss and Jacobi sums
Norm-restricted Gauss and Jacobi sums
Hypergeometric
character sums over finite fields
11T24
Quantum physics
33C05
Hasse–Davenport theorems
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Summary: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 ( mod 4 ) , and this paper provides such a proof for the remaining case q ≡ 3 ( mod 4 ) . Our proofs are valid for all characteristics p > 2 . Along the way we prove some elegant new character sum identities.
ISSN:2363-9555
2363-9555
DOI:10.1007/s40993-016-0071-5