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
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.
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
Affiliations des auteurs :
Stéphane Louboutin 1
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
@article{10_4064_cm90_1_6,
author = {St\'ephane Louboutin},
title = {The mean value of $|L(k,\chi)|^2$
at positive rational integers $k\ge 1$},
journal = {Colloquium Mathematicum},
pages = {69--76},
year = {2001},
volume = {90},
number = {1},
doi = {10.4064/cm90-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm90-1-6/}
}
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