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.
- Eisenstein sums
- Gauss and Jacobi sums
- Hasse–Davenport theorems
- Hypergeometric F character sums over finite fields
- Norm-restricted Gauss and Jacobi sums
- Quantum physics