Cluster Polylogarithms I: Quadrangular Polylogarithms
Algebraic Geometry
2022-11-08 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.2208.01564,
title = {Cluster Polylogarithms I: Quadrangular Polylogarithms},
author = {Andrei Matveiakin and Daniil Rudenko},
journal= {arXiv preprint arXiv:2208.01564},
year = {2022}
}