Colloquium – Talk by Alexander Dunn: October 7, 2025
October 7, 2025 (Wednesday), 4:10 pm
Alexander Dunn, Georgia Institute of Technology
Recent progress on Gauss sums and primes
Large sieve inequalities are a fundamental tool used to investigate prime numbers and exponential sums. In this Colloquium I will explain my work that resolves a 1978 conjecture of S. Patterson (conditional on the Generalized Riemann hypothesis) concerning the bias of cubic Gauss sums over the prime numbers. This explains a well-known numerical bias first observed by Kummer in 1846. This bias was later the subject of testing on some of the first super computers in the 20th century. Recent and related progress on higher order Gauss sums will also be outlined. This work sheds light on some of the mysteries surrounding large sieve inequalities and gives us clues on where to look next for more progress.
This is based on serval joint works with various collaborators: Maksym Radziwill, Chantal David, Alia Hamieh, and Hua Lin