The sixth power moment of Dirichlet L-functions

Abstract

We prove a formula, with power savings, for the sixth moment of Dirichlet L-functions averaged over moduli $q$, over primitive characters $\chi$ modulo $q$, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.

28 pages. Version 2 is a significant rewriting of Version 1. To appear in GAFA

References in corpus (3)

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

Cited by in corpus (3)

• Conjectures for the integral moments and ratios of L-functions over function fields
• Small gaps between zeros of twisted L-functions
• The eighth moment of Dirichlet $L$-functions