Moments of $L$-functions and Mean Values of Long Dirichlet Polynomials

Abstract: Establishing asymptotic formulae for moments of $L$-functions is a central theme in analytic number theory. This topic is related to various non-vanishing conjectures and the generalized Lindelöf Hypothesis. A major breakthrough in analytic number theory occurred in 1998 when Keating and Snaith established a conjectural formula for moments of the Riemann zeta function using ideas from random matrix theory. The methods of Keating and Snaith led to similar conjectures for moments of many families of $L$-functions. These conjectures have become a driving force in this field which has witnessed substantial progress in the last two decades. In this talk, I will review the history of this subject and survey some recent results. I will also discuss recent joint work with Nathan Ng on the mean values of long Dirichlet polynomials which could be used to model moments of the zeta function.

algebraic geometrynumber theory

Audience: researchers in the topic

Comments: Zoom Meeting ID: 856 1386 0958 Passcode: 513992

FGC-HRI-IPM Number Theory Webinars

Series comments: password is 848084