Paper
Multiple Elliptic Polylogarithms
Abstract
We study the de Rham fundamental group of the configuration space of marked points on an elliptic curve , and define multiple elliptic polylogarithms. These are multivalued functions on with unipotent monodromy, and are constructed by a general averaging procedure.
We show that all iterated integrals on , and in particular the periods of the unipotent fundamental group of the punctured curve , can be expressed in terms of these functions.