On the mean values of Dirichlet L -functions

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On the Mean Values of Dirichlet L-functions

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 and Keating for the Riemann zeta-function. This allows us to recover conjectures for the moments based on random matrix models, inc...

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N ov 2 00 6 On the mean values of Dirichlet L - functions

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 t...

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ژورنال

عنوان ژورنال: Proceedings of the London Mathematical Society

سال: 2007

ISSN: 0024-6115

DOI: 10.1112/plms/pdm008