Number Theory Seminar: David Belius (Univ. of Basel)

Extreme values of the Riemann Zeta function, and log-correlated Gaussian fields

I will describe how the Riemann Zeta function on the critical line can be viewed as a pseudo-random Gaussian field with a correlation function with logarithmic growth. Such log-correlated random fields have recently attracted considerable interest in probability theory. Fyodorv, Hiary and Keating conjectured several striking results about the extreme values of the Riemann Zeta function based on this connection. In this talk I will explain how a certain approximate tree structure in Dirichlet polynomials can be used to prove one of their conjectures, giving the asymptotics of the maximum of the magnitude of the function in a typical interval of length O(1).

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