English

Some mixed character sum identities of Katz II

Number Theory 2016-12-21 v2

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 (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.

Keywords

Cite

@article{arxiv.1609.01429,
  title  = {Some mixed character sum identities of Katz II},
  author = {Ron Evans and John Greene},
  journal= {arXiv preprint arXiv:1609.01429},
  year   = {2016}
}

Comments

21 pages, to appear in Research in Number Theory