Seth Hardy

Exponential sums with random multiplicative coefficients

The study of exponential sums with multiplicative coefficients is classical in analytic number theory, yet our understanding of them is far from complete. However, in recent years, our understanding of random multiplicative functions has flourished, and pioneering work has been conducted by Benatar, Nishry, and Rodgers to uncover how exponential sums typically behave when their coefficients are given by random multiplicative functions. In this talk, we will introduce random multiplicative functions, discuss some of the literature surrounding them, and outline recent work on obtaining uniform bounds for the size of exponential sums with random multiplicative coefficients.