Workshop: Moments of Dirichlet L-functions, Caroline Turnage-Butterbaugh

Speaker
Caroline Turnage-Butterbaugh, Carleton College

Abstract
I will outline how to harness the asymptotic large sieve to prove an asymptotic formula for the general 2kth moment of an approximation to the family of all Dirichlet L-functions of even primitive characters of bounded conductor. 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 diagonal terms in their conjectured asymptotic formula for this family of L-functions. This is joint work with Siegfred Baluyot.