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.
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