Negative moments of the Riemann zeta-function

Speaker: Alexandra Florea

Date: Mon, Dec 5, 2022

Location: PIMS, University of Lethbridge, Zoom, Online

Conference: Lethbridge Number Theory and Combinatorics Seminar

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory


Alexandra Florea (University of California Irvine, USA)

I will talk about recent work towards a conjecture of Gonek regarding negative shifted moments of the Riemann zeta-function. I will explain how to obtain asymptotic formulas when the shift in the Riemann zeta function is big enough, and how we can obtain non-trivial upper bounds for smaller shifts. I will also discuss some applications to the question of obtaining cancellation of averages of the Mobius function. Joint work with H. Bui.