Title: Sharp bounds for moments of the Riemann zeta function
Speaker: Adam Harper, University of Cambridge
Seminar Type: Number Theory
Abstract: The Riemann zeta function \(\zeta(s)\) has been studied for more than 150 years, but our knowledge about it remains very incomplete. On or near the critical line \(\Re(s)=1/2\), our knowledge is lacking even if we assume the truth of the Riemann Hypothesis. For example, the behaviour of the power moments \(\int_0^T |\zeta(1/2+it)|^{2k} dt\), which is subject to precise conjectures coming from random matrix theory, has resisted most rigorous study until recently.
In this talk I will try to explain work of Soundararajan, which gave nearly sharp upper bounds for the moments of zeta (assuming the Riemann Hypothesis), and also my recent improvement giving sharp upper bounds (assuming the Riemann Hypothesis).
