Fractions de Bernoulli-Carlitz et opérateurs q-Zeta
Journal de Théorie des Nombres de Bordeaux, Tome 22 (2010) no. 3, pp. 575-581.

On introduit une déformation des séries de Dirichlet d’une variable complexe s, sous la forme d’un opérateur pour chaque nombre complexe s, agissant sur les séries formelles sans terme constant en une variable q. On montre que les fractions de Bernoulli-Carlitz sont les images de certains polynômes en q par les opérateurs associés à la fonction ζ de Riemann aux entiers négatifs.

Bernoulli-Carlitz fractions and q-Zeta operators

We introduce a deformation of Dirichlet series of one complex variable s, which is given for each complex number s by an operator acting on formal power series without constant term in the variable q. We prove that the Bernoulli-Carlitz fractions are obtained as the image of some simple polynomials in q by the operators corresponding to the Riemann ζ function at negative integers.

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DOI : https://doi.org/10.5802/jtnb.733
@article{JTNB_2010__22_3_575_0,
     author = {Fr\'ed\'eric Chapoton},
     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 = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.733/}
}
Frédéric Chapoton. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.733/

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