## Probability Seminar

Joseph NajnudelUniversity of Cincinnati
On the extreme values of the Riemann zeta function on random intervals of the critical line
Friday, March 9, 2018 - 12:15pm
Malott 205

In this talk, we study the maximum of the real and the imaginary part of the logarithm of the Riemann zeta function on random intervals of the critical line. We sketch a proof of the fact that if these intervals are centered at 1/2 + i UT, U being uniformly distributed on [0,1], then the maximum, divided by log log T, tends to 1 in probability. This proves a weak version of a conjecture by Fyodorov, Hiary and Keating.