Quartic Gauss sums over primes and metaplectic theta functions

Speaker

Alex Dunn (Georgia Tech)

Date

Wed, Nov 6 2024, 1:00pm

Location

383N

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 the Gaussian quadratic field, 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. This is a joint work with C.David, A.Hamieh, and H.Lin.