Iterated integrals on products of one variable multiple polylogarithms

Abstract

In this paper, we show that the iterated integrals on products of one variable multiple polylogarithms from [Formula: see text] to [Formula: see text] are actually in the algebra of multiple zeta values if they are convergent. In the divergent case, we define the regularized iterated integrals from [Formula: see text] to [Formula: see text]. By the same method, we show that the regularized iterated integrals are also in the algebra of multiple zeta values. As an application, we give new series representations for multiple zeta values and calculate some interesting examples of iterated integrals.