论文标题
关于通过计算机对几个复杂可变Zeta函数的全局重归化和正则化
On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer
论文作者
论文摘要
这篇综述涉及解决Zeta函数组合方面的Zeta函数组合方面的knizhnik-Zamolodchikov方程（$ KZ_3 $）的特殊情况，这些案例对非交通符号计算的几个变量和软件。特别是，我们描述了$（kz_3）$的实际解决方案，从而导致唯一的非交换系列，$φ_{kz} $，所谓的drinfel'd Associator（或Drinfel'd系列）。由于代数结构和多组阶层和谐波和谐波和谐波总和的奇异性分析，还明确提供了具有合理系数的非平凡表达式，以$φ_{kz} $满足相同的属性。
This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations ($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.
