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arXiv · 0710.5176

The sixth power moment of Dirichlet L-functions

J. B. Conrey·H. Iwaniec·K. Soundararajan
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Abstract

We prove a formula, with power savings, for the sixth moment of Dirichlet L-functions averaged over moduli $q$, over primitive characters $χ$ 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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J. B. Conrey, H. Iwaniec, K. Soundararajan. 2012-02-12. The sixth power moment of Dirichlet L-functions. https://arxiv.org/abs/0710.5176

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