Iterated integrals on [formula omitted] and a class of relations among multiple zeta values

Abstract

In this paper we consider iterated integrals on P1∖{0,1,∞,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.