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Number Theory Seminar

Event Type
Department of Mathematics
Literature, Cultures, and Linguistics Building, Room G-32
Nov 28, 2023   11:00 - 11:50 am  
Caroline Turnage-Butterbaugh (Carleton College)
Jesse Thorner and Yuan Liu
jat9@illinois.edu and yyyliu@illinois.edu
Originating Calendar
Number Theory Seminar Calendar
Title: Moments of Dirichlet L-functions 

Abstract: In recent decades there has been much interest and measured progress in the study of moments of the Riemann zeta-function and, more generally, of various L-functions. Despite a great deal of effort spanning over a century, asymptotic formulas for moments of L-functions remain stubbornly out of reach in all but a few cases. In this talk, we consider the problem for the family of all Dirichlet L-functions of even primitive characters of bounded conductor. I will outline how to harness the asymptotic large sieve to prove an asymptotic formula for the general 2kth moment of an approximation to this family. The result, which assumes the generalized Lindelöf hypothesis for large values of k, agrees with the prediction of Conrey, Farmer, Keating, Rubenstein, and Snaith. Moreover, it provides the first rigorous evidence beyond the so-called “diagonal terms” in their conjectured asymptotic formula for this family of L-functions.
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