Number Theory Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Altgeld Hall 347
- Date
- Feb 27, 2024 11:00 - 11:50 am
- Speaker
- Alexander Dunn (Georgia Institute of Technology)
- Contact
- Jesse Thorner and Yuan Liu
- jat9@illinois.edu and yyyliu@illinois.edu
- Views
- 57
- Originating Calendar
- Number Theory Seminar Calendar
Title: Quartic Gauss sums over primes and metaplectic theta functions
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 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.