On the mean values of Dirichlet L-functions
Number Theory
2012-11-06 v3
Abstract
We study the 2k-th power moment of Dirichlet L-functions L(s,\chi) at the centre of the critical strip (s=1/2), where the average is over all primitive characters \chi (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes & Keating for the Riemann zeta function. This allows us to recover conjectures for the moments based on random matrix models, incorporating the arithmetical terms in a natural way.
Cite
@article{arxiv.math/0607199,
title = {On the mean values of Dirichlet L-functions},
author = {H. M. Bui and J. P. Keating},
journal= {arXiv preprint arXiv:math/0607199},
year = {2012}
}