Iterated integrals on products of one variable multiple polylogarithms
Number Theory
2020-06-09 v3
Abstract
In this paper we show that the iterated integrals on products of one variable multiple polylogarithms from 0 to 1 are actually multiple zeta values if they are convergent. In the divergent case, we define regularized iterated integrals from 0 to 1. By the same method, we show that the regularized iterated integrals are also multiple zeta values. As an application, we give new series representations for multiple zeta values and calculate some interesting examples of iterated integrals.
Cite
@article{arxiv.1906.02018,
title = {Iterated integrals on products of one variable multiple polylogarithms},
author = {Jiangtao Li},
journal= {arXiv preprint arXiv:1906.02018},
year = {2020}
}
Comments
18 pages