Jad Hamdan

The Fyodorov–Hiary–Keating conjecture on mesoscopic intervals

We derive precise upper bounds for the maximum of the Riemann zeta function on a typical short interval of the critical line. We show that for fixed θ∈(−1,0], large T, and y≥2 satisfying y=O(loglogT/logloglogT), the proportion of points t∈[T,2T] for which max|h|≤logθT|ζ(12+it+ih)...