Quartic Gauss sums over primes and metaplectic theta functions
Chantal David, Alexander Dunn, Alia Hamieh, Hua Lin
Published: 2023/6/20
Abstract
We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve over $\mathbb{Q}(i)$, and Suzuki's evaluation of the Fourier-Whittaker coefficients of quartic theta functions at squares. We also conjecture asymptotics for certain moments of quartic Gauss sums over primes.