On the mean values of Dirichlet L-functions

Details On the mean values of Dirichlet L-functions On the mean values of Dirichlet L-functions

2006-07-07

arxiv.org/abs/math/0607199v3

Proc. London Math. Soc. 95 (2007), 273--298

Mathematics

Number Theory

Scientific paper

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.

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