Cluster Polylogarithms I: Quadrangular Polylogarithms
arXiv:2208.01564
Abstract
We suggest a definition of cluster polylogarithms on an arbitrary cluster variety and classify them in type . We find functional equations for multiple polylogarithms which generalize equations discovered by Abel, Kummer, and Goncharov to an arbitrary weight. As an application, we prove a part of the Goncharov depth conjecture in weight six.