A+ CATEGORY SCIENTIFIC UNIT

The mean value of $|L(k,\chi)|^2$ at positive rational integers $k\ge 1$

Volume 90 / 2001

Stéphane Louboutin Colloquium Mathematicum 90 (2001), 69-76 MSC: Primary 11M06, 11M20, 11R18. DOI: 10.4064/cm90-1-6

Abstract

Let $k\ge 1$ denote any positive rational integer. We give formulae for the sums $$ S_{\rm odd}(k,f) =\sum _{\chi (-1)=-1}| L(k,\chi )| ^2 $$ (where $\chi $ ranges over the $\phi (f)/2$ odd Dirichlet characters modulo $f>2$) whenever $k\ge 1$ is odd, and for the sums $$ S_{\rm even}(k,f) =\sum _{\chi (-1)=+1} | L(k,\chi )| ^2 $$ (where $\chi $ ranges over the $\phi (f)/2$ even Dirichlet characters modulo $f>2$) whenever $k\ge 1$ is even.

Authors

  • Stéphane LouboutinInstitut de Mathématiques de Luminy, UPR 9016
    163, avenue de Luminy
    Case 907
    13288 Marseille Cedex 9, France
    e-mail

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