Better than squareroot cancellation in number theory

Abstract

We give a short survey of the phenomenon of better than squareroot cancellation, specifically as it applies to averages of multiplicative character sums (such as $\frac{1}{r-1}{\sum }_{\ddot{I}‡\text{mod}r}|{\sum }_{n\le x}\ddot{I}‡(n){|}^{2q}$) thanks to their connection with so-called multiplicative chaos. We focus on the number theoretic aspects of the arguments, and also touch on some possible applications.

27 pages. A version of this paper will appear in the Proceedings of the ICM 2026