Geodesic
The mean value of $|L(k,\chi)|^2$ at positive rational integers $k\ge 1$
Stéphane Louboutin1
1 Institut de Mathématiques de Luminy, UPR 9016 163, avenue de Luminy Case 907 13288 Marseille Cedex 9, France
Colloquium Mathematicum, Tome 90 (2001) no. 1, pp. 69-76.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm90-1-6
Keywords: denote positive rational integer formulae sums odd sum chi chi where chi ranges phi odd dirichlet characters modulo whenever odd sums even sum chi chi where chi ranges phi even dirichlet characters modulo whenever even

Stéphane Louboutin 1

1 Institut de Mathématiques de Luminy, UPR 9016 163, avenue de Luminy Case 907 13288 Marseille Cedex 9, France 
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Stéphane Louboutin. The mean value of $|L(k,\chi)|^2$
at positive rational integers $k\ge 1$. Colloquium Mathematicum, Tome 90 (2001) no. 1, pp. 69-76. doi : 10.4064/cm90-1-6. http://geodesic.mathdoc.fr/articles/10.4064/cm90-1-6/

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