Louis-Pierre Arguin

Conditional Upper Bounds on the Moments and Large Deviations of the Riemann Zeta Function

In this talk, I will present a proof that the measures of level sets of the Riemann zeta function have Gaussian tail, up to a constant C, for values in suitable regimes, conditionally on the Riemann Hypothesis. As a corollary, we recover the best-known upper bounds of Harper on the moments on the critical line. The proof relies on the recursive scheme of prior work with Bourgade & Radziwill that is inspired by a random walk heuristic. It also combines ideas of Soundararajan and Harper. We will discuss possible improvements to the constant C as well as the connections with the Keating-Snaith Conjecture from Random Matrix Theory for the optimal constant. This is joint work with Emma Bailey & Asher Roberts.