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.
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.
@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://archive.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://archive.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://archive.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, Volume 22 (2010) no. 3, pp. 575-581. doi : 10.5802/jtnb.733. http://archive.numdam.org/articles/10.5802/jtnb.733/
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