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Number Theory Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
Literature, Cultures, and Linguistics Building, Room G-32
Date
Nov 28, 2023   11:00 - 11:50 am  
Speaker
Caroline Turnage-Butterbaugh (Carleton College)
Contact
Jesse Thorner and Yuan Liu
E-Mail
jat9@illinois.edu and yyyliu@illinois.edu
Views
24
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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