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arXiv · 2009.03931

Families of eulerian functions involved in regularization of divergent polyzetas

V. C. Bui·V. Hoang Ngoc Minh·V. Nguyen Dinh·Q. H. Ngo
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Abstract

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 $ζ(2k)/π^{2k}$ and their multiindexed generalization, we will obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of noncommutative rational series. The same combinatorial frameworks also allow to study the independence of a family of eulerian functions.

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V. C. Bui, V. Hoang Ngoc Minh, V. Nguyen Dinh, Q. H. Ngo. 2023-02-26. Families of eulerian functions involved in regularization of divergent polyzetas. https://arxiv.org/abs/2009.03931

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