Families of eulerian functions involved in regularization of divergent polyzetas

2020/09/08 by Văn Chiến Bùi, Bui, V. C., Minh, V. Hoang Ngoc +2 · 2 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.2009.03931

openalex publication_date 2020/09/08 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28

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.

Cited by

• Hyperlogarithms: Functions on Free Monoids
• On the Algebraic Bases of Polyzetas

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