Emma Bailey (CUNY)

Title:Upper and lower bounds for the large deviations of Selberg’s central limit theorem.

Abstract: 

Suppose we form a complex random variable by taking a uniform random variable U on [T, 2T] and evaluating the Riemann zeta function at that height on the critical line, 1/2 + i U. Selberg’s central limit theorem informs us that the real (or indeed the imaginary) part of the logarithm of this random variable behaves, as T grows, like a centred Gaussian with a particular variance. It is of interest to the number theoretic community, in particular in relation to the moments of the Riemann zeta function, to understand the large deviations of this random variable. In this talk I will discuss the case for the right tail, presenting upper (2023) and lower (2024) bounds in work joint with L-P Arguin.

The talk will not require prior number theoretic knowledge.