On introduit une déformation des séries de Dirichlet d’une variable complexe , sous la forme d’un opérateur pour chaque nombre complexe , agissant sur les séries formelles sans terme constant en une variable . On montre que les fractions de Bernoulli-Carlitz sont les images de certains polynômes en par les opérateurs associés à la fonction de Riemann aux entiers négatifs.
Bernoulli-Carlitz fractions and -Zeta operators
We introduce a deformation of Dirichlet series of one complex variable , which is given for each complex number by an operator acting on formal power series without constant term in the variable . We prove that the Bernoulli-Carlitz fractions are obtained as the image of some simple polynomials in by the operators corresponding to the Riemann function at negative integers.
@article{JTNB_2010__22_3_575_0,
author = {Chapoton, Fr\'ed\'eric},
title = {Fractions de {Bernoulli-Carlitz} et op\'erateurs $q${-Zeta}},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {575--581},
publisher = {Universit\'e Bordeaux 1},
volume = {22},
number = {3},
year = {2010},
doi = {10.5802/jtnb.733},
zbl = {1267.11097},
mrnumber = {2769332},
language = {fr},
url = {http://www.numdam.org/articles/10.5802/jtnb.733/}
}
TY - JOUR AU - Chapoton, Frédéric TI - Fractions de Bernoulli-Carlitz et opérateurs $q$-Zeta JO - Journal de théorie des nombres de Bordeaux PY - 2010 SP - 575 EP - 581 VL - 22 IS - 3 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.733/ DO - 10.5802/jtnb.733 LA - fr ID - JTNB_2010__22_3_575_0 ER -
%0 Journal Article %A Chapoton, Frédéric %T Fractions de Bernoulli-Carlitz et opérateurs $q$-Zeta %J Journal de théorie des nombres de Bordeaux %D 2010 %P 575-581 %V 22 %N 3 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.733/ %R 10.5802/jtnb.733 %G fr %F JTNB_2010__22_3_575_0
Chapoton, Frédéric. Fractions de Bernoulli-Carlitz et opérateurs $q$-Zeta. Journal de théorie des nombres de Bordeaux, Tome 22 (2010) no. 3, pp. 575-581. doi : 10.5802/jtnb.733. http://www.numdam.org/articles/10.5802/jtnb.733/
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