On the logarithm of the Riemann zeta-function near the nontrivial zeros

Abstract: Selberg's central limit theorem is one of the most significant probabilistic results in analytic number theory. Roughly, it states that the logarithm of the Riemann zeta-function on and near the critical line has an approximate two-dimensional Gaussian distribution.

In this talk, we will talk about our recent result which states that the distribution of the logarithm of the Riemann zeta-function near the sequence of the nontrivial zeros has a similar central limit theorem. Our results are conditional on the Riemann Hypothesis and/or suitable zero-spacing hypotheses. They also have suitable generalizations to Dirichlet $L$-functions.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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