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arXiv · 2208.01564

Cluster Polylogarithms I: Quadrangular Polylogarithms

Andrei Matveiakin·Daniil Rudenko
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Abstract

We suggest a definition of cluster polylogarithms on an arbitrary cluster variety and classify them in type $A$. 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.

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Andrei Matveiakin, Daniil Rudenko. 2022-08-02. Cluster Polylogarithms I: Quadrangular Polylogarithms. https://arxiv.org/abs/2208.01564

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