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arXiv · 2209.09849

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

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

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations ($KZ_3$) 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 $(KZ_3)$ 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.

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V. C. Bui, V. Hoang Ngoc Minh, V. Nguyen Dinh, Q. H. Ngo. 2023-08-22. On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer. https://arxiv.org/abs/2209.09849

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