Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line

By L. Arguin, David Belius, P. Bourgade, Maksym Radziwill, Kannan Soundararajan. Communications on Pure and Applied Mathematics, 2016

107 citations recorded by the source corpus.

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. © 2018 Wiley Periodicals, Inc.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8a23b547c5b8f2dc7d282c0abd4b59e4a8307a6f

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

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Citations in the corpus

On the extreme values of the Riemann zeta function on random intervals of the critical line (2016, methodology): “Remark After the first submission of the present paper to arXiv.org, our result concerning the real part of zeta has been proven by Arguin, Belius, Bourgade, Radziwi l l and Soundararajan [4], without assuming the Riemann hypothesis.”
The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line (2016, background): “[3, 68] (see also [2, 70, 22] for related results in the setting of random matrices).”