The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan]

Abstract

This is the text to accompany my Bourbaki seminar from 30th March 2019, on the maximum size of the Riemann zeta function in "almost all" intervals of length 1 on the critical line. It surveys the conjecture of Fyodorov--Hiary--Keating on the behaviour of this typical maximum, as well as recent progress towards the conjecture by Najnudel and by Arguin--Belius--Bourgade--Radziwiłł--Soundararajan. There is also some general background discussion of the value distribution and large values of zeta.

arXiv comment22 pages

References in corpus (3)

• Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
• Extreme values of the Riemann zeta function and its argument
• Moments of the Riemann zeta function on short intervals of the critical line

Cited by in corpus (6)

• On the partition function of the Riemann zeta function, and the Fyodorov--Hiary--Keating conjecture
• The Fyodorov-Hiary-Keating Conjecture. I
• On the moments of the moments of $\zeta (1/2+it)$
• On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices
• Maxima of log-correlated fields: some recent developments
• Higher moments of distribution of zeta zeros