Seth Hardy

Character sums over smooth numbers

Partial sums of Dirichlet characters are a classical object of study in analytic number theory. In recent years, our understanding of the "typical" behaviour of these sums has vastly improved, driven largely by advances of Harper in the study of random multiplicative functions and their connection to "critical Gaussian multiplicative chaos". Given these advances, one may ask whether partial sums of characters and random multiplicative functions also give rise to interesting phenomena when restricted to other sets. In this talk, I will discuss how character sums restricted to smooth numbers (that is, numbers whose prime factors are restricted to be below some threshold) often exhibit far more cancellation than the full partial sums. This is joint work with Max Wenqiang Xu.