The mean value of |L(k,χ)|² at positive rational integers k ≥ 1

Stéphane Louboutin. "The mean value of |L(k,χ)|² at positive rational integers k ≥ 1." Colloquium Mathematicae 90.1 (2001): 69-76. <http://eudml.org/doc/284180>.

@article{StéphaneLouboutin2001,
abstract = {Let k ≥ 1 denote any positive rational integer. We give formulae for the sums $S_\{odd\}(k,f) = ∑_\{χ(-1)=-1\} |L(k,χ)|²$ (where χ ranges over the ϕ(f)/2 odd Dirichlet characters modulo f > 2) whenever k ≥ 1 is odd, and for the sums $S_\{even\}(k,f) = ∑_\{χ(-1) = +1\} |L(k,χ)|²$ (where χ ranges over the ϕ(f)/2 even Dirichlet characters modulo f>2) whenever k ≥ 1 is even.},
author = {Stéphane Louboutin},
journal = {Colloquium Mathematicae},
keywords = {mean-square formula},
language = {eng},
number = {1},
pages = {69-76},
title = {The mean value of |L(k,χ)|² at positive rational integers k ≥ 1},
url = {http://eudml.org/doc/284180},
volume = {90},
year = {2001},
}

TY - JOUR
AU - Stéphane Louboutin
TI - The mean value of |L(k,χ)|² at positive rational integers k ≥ 1
JO - Colloquium Mathematicae
PY - 2001
VL - 90
IS - 1
SP - 69
EP - 76
AB - Let k ≥ 1 denote any positive rational integer. We give formulae for the sums $S_{odd}(k,f) = ∑_{χ(-1)=-1} |L(k,χ)|²$ (where χ ranges over the ϕ(f)/2 odd Dirichlet characters modulo f > 2) whenever k ≥ 1 is odd, and for the sums $S_{even}(k,f) = ∑_{χ(-1) = +1} |L(k,χ)|²$ (where χ ranges over the ϕ(f)/2 even Dirichlet characters modulo f>2) whenever k ≥ 1 is even.
LA - eng
KW - mean-square formula
UR - http://eudml.org/doc/284180
ER -