The eighth moment of Dirichlet $L$-functions

Abstract

We prove an asymptotic for the eighth moment of Dirichlet $L$-functions averaged over primitive characters $\chi$ modulo $q$, over all moduli $q\le Q$ and with a short average on the critical line, conditionally on GRH. We derive the analogous result for the fourth moment of Dirichlet twists of GL(2) L-functions. Our results match the moment conjectures in the literature; in particular, the constant 24024 appears as a factor in the leading order term of the eighth moment.

31 pgs. Minor revisions

References in corpus (3)

• Lower bounds for moments of L-functions
• A conjecture for the sixth power moment of the Riemann zeta-function
• The sixth power moment of Dirichlet L-functions