Hybrid Statistics of the Maxima of a Random Model of the Zeta Function over Short Intervals
Speaker: Christine K. Chang
Date: Tue, Oct 8, 2024
Location: PIMS, University of British Columbia, Zoom, Online
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Tue, Oct 8, 2024
Location: PIMS, University of British Columbia, Zoom, Online
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
We will present a matching upper and lower bound for the right tail
probability of the maximum of a random model of the Riemann zeta function over
short intervals. In particular, we show that the right tail interpolates
between that of log-correlated and IID random variables as the interval varies
in length. We will also discuss a new normalization for the moments over short
intervals. This result follows the recent work of Arguin-Dubach-Hartung and is inspired by a conjecture by Fyodorov-Hiary-Keating on the local maximum over
short intervals.
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