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On the mean values of Dirichlet L ‐functions
Author(s) -
Bui H. M.,
Keating J. P.
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm008
Subject(s) - mathematics , arithmetic function , dirichlet distribution , riemann zeta function , dirichlet series , hadamard product , euler's formula , analytic number theory , product (mathematics) , pure mathematics , hadamard transform , combinatorics , mathematical analysis , geometry , boundary value problem
We study the 2 k 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, incorporating the arithmetical terms in a natural way.