The sixth power moment of Dirichlet L-functions

Details The sixth power moment of Dirichlet L-functions The sixth power moment of Dirichlet L-functions

2007-10-26

arxiv.org/abs/0710.5176v2

Mathematics

Number Theory

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

Scientific paper

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.

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