[Familles de fonctions eulériennes impliquées dans la régularisation de polyzêtas divergents]
Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton–Girard identity) for the complex Gamma function, we are interested in the ratios of and their multiindexed generalization, we obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of words and noncommutative rational series. The same frameworks also allow to study the independence of a family of eulerian functions.
En généralisant les fonctions euleriennes, nous étudions leurs relations avec la fonction zêta en plusieurs variables. En particulier, à partir du théorème de factorisation de Weierstrass (et l’identité de Newton-Girard) pour la fonction Gamma complexe, nous nous intéressons aux rapports et leurs généralisations. Nous obtenons une situation analogue et nous tirerons quelques conséquences sur une structure de l’algèbre des valeurs polyzêtas, au moyen de la combinatoire des mots et des séries rationnelles en variables non commutatifs. Le même cadre de travail permet également d’étudier l’indépendance d’une famille de fonctions euleriennes.
Keywords: Eulerian functions, zeta function, Gamma function
Bui, V. C. 1 ; Hoang Ngoc Minh, V. 2 ; Ngo, Q. H. 3 ; Nguyen Dinh, V. 4
CC-BY-ND 4.0
@article{PMB_2023____5_0,
author = {Bui, V. C. and Hoang Ngoc Minh, V. and Ngo, Q. H. and Nguyen Dinh, V.},
title = {Families of eulerian functions involved in regularization of divergent polyzetas},
journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
pages = {5--28},
year = {2023},
publisher = {Presses universitaires de Franche-Comt\'e},
doi = {10.5802/pmb.47},
language = {en},
url = {https://www.numdam.org/articles/10.5802/pmb.47/}
}
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%0 Journal Article %A Bui, V. C. %A Hoang Ngoc Minh, V. %A Ngo, Q. H. %A Nguyen Dinh, V. %T Families of eulerian functions involved in regularization of divergent polyzetas %J Publications mathématiques de Besançon. Algèbre et théorie des nombres %D 2023 %P 5-28 %I Presses universitaires de Franche-Comté %U https://www.numdam.org/articles/10.5802/pmb.47/ %R 10.5802/pmb.47 %G en %F PMB_2023____5_0
Bui, V. C.; Hoang Ngoc Minh, V.; Ngo, Q. H.; Nguyen Dinh, V. Families of eulerian functions involved in regularization of divergent polyzetas. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2023), pp. 5-28. doi: 10.5802/pmb.47
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