In this talk we discuss recent joint work with Chantal David, Alex Dunn and Hua Lin on estimates for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including the use of quadratic large sieve over $\mathbb{Q}(i)$, and Suzuki's evaluation of the Fourier-Whittaker coefficients of quartic theta functions at squares.

Bio: Alia Hamieh is an Associate Professor in the Department of Mathematics and Statistics at the University of Northern British Columbia. She earned her PhD from UBC in 2013, under the supervision of Vinayak Vatsal.

Her research interests are in analytic number theory, modular forms, central values of automorphic L‑functions and Rankin-Selberg convolutions.