Some mixed character sum identities of Katz II
Ron Evans, John Greene · Research in Number Theory · 2017
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 $$q \equiv 1 \pmod 4$$ , and this paper provides such a proof for the remaining case $$q \equiv 3 \pmod 4$$ . Our proofs are valid for all characteristics $$p>2$$ . Along the way we prove some elegant new character sum identities.