Bounds on exponential sums have been an important topic of study in Analytic Number Theory, offering solutions to many problems, including the famous Ternary Goldbach Conjecture and Fermat's Last Theorem. In 2006, L. Zhao published a paper finding bounds on a particular exponential sum with square root amplitude, twisted with Hecke-eigenvalues over the full modular group. In this talk I will present some history of these sums, as well as demonstrating more explicit constants for the bounds found by Zhao, and finally an extension of these bounds to the congruence subgroups.
Thursday 21 April 2022, 12pm
Pure Maths Seminar