On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer

2022/09/18 by V. C. Bui, V. Hoang Ngoc Minh, Bui, V. C. +5 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2209.09849

openalex publication_date 2022/09/18 · openalex created_date 2022/09/23 · openalex updated_date 2026/07/28

Abstract

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations (KZ₃) using our recent results on combinatorial aspects of zeta functions on several variables and software on noncommutative symbolic computations. In particular, we describe the actual solution of (KZ₃) leading to the unique noncommutative series, Φ_KZ, so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions for series with rational coefficients, satisfying the same properties with Φ_KZ, are also explicitly provided due to the algebraic structure and the singularity analysis of the polylogarithms and harmonic sums.

Cited by

• Multiple polylogarithms at non-positive indices and combinatorics of Magnus polynomials

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