Katz II的混合character和恒等式
Some mixed character sum identities of Katz II
摘要：
一个与量子物理学有关的猜想使N. Katz发现了一些令人惊奇的混合特征和恒等式，其中q是素数p > 3的幂。他的证明需要深刻的代数几何技术，他表示有兴趣找到一个更直接的直接证明。第一作者最近给出了这样一个证明他的身份时，q = 1（mod 4），本文提供了这样一个证明的其余情况下，q = 3（mod 4）。我们的证明对所有特征p > 2都是有效的。一路上，我们证明了一些优雅的新的字符和身份。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
