N ov 2 00 6 On the mean values of Dirichlet L - functions
نویسنده
چکیده
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 arith-metical terms in a natural way.
منابع مشابه
A pr 2 00 8 October 16 , 2008 MEAN VALUES WITH CUBIC CHARACTERS
We investigate various mean value problems involving order three primitive Dirichlet characters. In particular, we obtain an asymptotic formula for the first moment of central values of the Dirichlet L-functions associated to this family, with a power savings in the error term. We also obtain a large-sieve type result for order three (and six) Dirichlet characters.
متن کامل2 00 6 On the mean values of Dirichlet L - functions H . M . BUI and J . P . KEATING School of Mathematics University of Bristol Bristol
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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