Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length

Zoom Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

Recently there has been considerable progress in probability and in number theory to understand the large values of the zeta function in small intervals of the critical line.
In this talk we consider a random model of the Riemann zeta function on the critical axis and study its maximum over intervals of length $(\log T)^\theta$, where $\theta$  is either fixed or tends to zero at a suitable rate. This has interesting connections with the extreme value statistics of IID and log-correlated random variables.
A key ingredient of the proof is a precise upper tail tightness estimate for the maximum of the model on intervals of size one, that includes a Gaussian correction. The is based on joint work with L.-P. Arguin (CUNY) and G. Dubach (IST Austria).