Affiliation:
1. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan Province, P. R. China
Abstract
Classical multiple zeta values can be viewed as iterated integrals of the differentials [Formula: see text] from [Formula: see text] to [Formula: see text]. In this paper, we reprove Brown’s theorem: For [Formula: see text], the iterated integral of the form [Formula: see text] is a [Formula: see text]-linear combination of multiple zeta values of weight [Formula: see text] if convergent. What is more, we show that if [Formula: see text] are in a [Formula: see text]-algebra generated by multiple polylogarithms and their dual, and if [Formula: see text], are in a [Formula: see text]-algebra generated by logarithm, then the iterated integral [Formula: see text] is a [Formula: see text]-linear combination of multiple zeta values. As an application of our main results, we show that the coefficients of the Taylor expansions of the Selberg integrals [Formula: see text] (with respect to [Formula: see text]) at the integral points in some product of right half complex plane are [Formula: see text]-linear combinations of multiple zeta values for any [Formula: see text] This statement generalizes Terasoma’s original result.
Funder
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory