Iterated integrals on P-1 {0, 1, infinity, z} and a class of relations among multiple zeta values

摘要

In this paper we consider iterated integrals on P-1 {0, 1, infinity, z} and define a class of Q-linear relations among them, which arises from the differential structure of the iterated integrals with respect to z. We then define a new class of Q-linear relations among the multiple zeta values by taking their limits of z -> 1, which we call confluence relations (i.e., the relations obtained by the confluence of two punctured points). One of the significance of the confluence relations is that it gives a rich family and seems to exhaust all the linear relations among the multiple zeta values. As a good reason for this, we show that confluence relations imply both the regularized double shuffle relations and the duality relations. (C) 2019 Published by Elsevier Inc.