Maximum of the Riemann zeta function on a short interval of the critical line

Abstract

We prove the leading order of a conjecture by Fyodorov, Hiary and Keating, about the maximum of the Riemann zeta function on random intervals along the critical line. More precisely, as T→∞ for a set of t∈[T,2T] of measure (1−o(1))T, we have max|t−u|≤1log∣∣ζ(12+iu)∣∣=(1+o(1))loglogT.

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