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A twisted quadratic moment for Dirichlet $ L$-functions


Author: Stéphane R. Louboutin
Journal: Proc. Amer. Math. Soc. 142 (2014), 1539-1544
MSC (2010): Primary 11M20
Published electronically: February 12, 2014
MathSciNet review: 3168461
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Abstract: Given $ c$, a positive integer, we give an explicit formula for the quadratic moments

$\displaystyle \sum _{\chi \in X_f^-}\chi (c)\vert L(1,\chi )\vert ^2,$

where $ X_f^-$ is the set of the odd Dirichlet characters mod $ f$ with $ f>2$.

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Additional Information

Stéphane R. Louboutin
Affiliation: Aix-Marseille Université, Institut de Mathématiques de Luminy, FRE 3529, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, France
Email: stephane.louboutin@univ-amu.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11721-7
Keywords: $L$-function, character, mean values, moments
Received by editor(s): January 27, 2012
Received by editor(s) in revised form: February 17, 2012, and June 12, 2012
Published electronically: February 12, 2014
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2014 American Mathematical Society