Some mixed character sum identities of Katz II

Ron Evans, John Greene

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish (US)
Article number8
JournalResearch in Number Theory
Volume3
Issue number1
DOIs
StatePublished - Dec 1 2017

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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