Rencontres de théorie analytique des nombres

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

by Lisa Hartung (Mainz Universität)

Salle Grisvard, IHP, 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. 

Organized by

Régis de la Bretèche