Maxima of a random model of the Riemann zeta function on longer intervals (and branching random walks)

par Lisa Hartung (Mainz Universität)

lundi 9 oct. 2023, 15:30 → 16:30 Europe/Paris

Salle Grisvard, IHP, Paris

We study the maximum of a random model for the Riemann zeta function (on the critical line at height $T$) on the interval $[-(\log T{)}^{\theta },(\log T{)}^{\theta })$, where $\theta =(\log \log T{)}^{-a}$, with $0<a<1$. We obtain the leading order as well as the logarithmic correction of the maximum. As it turns out, a good toy model is a collection of independent BRW’s, where the number of independent copies depends on $\theta$. In this talk I will try to
motivate our results by mainly focusing on this toy model.

The talk is based on joint work in progress with L.-P. Arguin and G. Dubach.