English

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

Combinatorics 2023-08-23 v3

Abstract

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations (KZ3KZ_3) 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)(KZ_3) leading to the unique noncommutative series, ΦKZ\Phi_{KZ}, so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions for series with rational coefficients, satisfying the same properties with ΦKZ\Phi_{KZ}, are also explicitly provided due to the algebraic structure and the singularity analysis of the polylogarithms and harmonic sums.

Keywords

Cite

@article{arxiv.2209.09849,
  title  = {On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer},
  author = {V. C. Bui and V. Hoang Ngoc Minh and V. Nguyen Dinh and Q. H. Ngo},
  journal= {arXiv preprint arXiv:2209.09849},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:2008.10872

R2 v1 2026-06-28T01:45:22.242Z