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On the mean values of Dirichlet L-functions

H. M. Bui·J. P. Keating
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Abstract

We study the 2k-th power moment of Dirichlet L-functions L(s,χ) at the centre of the critical strip (s=1/2), where the average is over all primitive characters χ(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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H. M. Bui, J. P. Keating. 2009-03-24. On the mean values of Dirichlet L-functions. https://arxiv.org/abs/math/0607199

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