Thursday, January 28 2021
15:30 - 16:30

IMSc Webinar

On the Logarithm of the Riemann Zeta-function Near the Nontrivial Zeros

Fatma Cicek

IIT Gandhinagar

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.

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