Cluster Polylogarithms I: Quadrangular Polylogarithms

Andrei Matveiakin; Daniil Rudenko

Cluster Polylogarithms I: Quadrangular Polylogarithms

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arxiv 2208.01564 v2 pith:SRL4C2M2 submitted 2022-08-02 math.AG math.NT

Cluster Polylogarithms I: Quadrangular Polylogarithms

Andrei Matveiakin , Daniil Rudenko This is my paper

classification math.AG math.NT

keywords polylogarithmsclusterarbitraryequationsgoncharovweightabelapplication

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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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de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs
hep-th 2026-05 unverdicted novelty 6.0

The n-site chain graph contribution to the de Sitter cosmological wavefunction in conformally coupled φ³ theory is expressed explicitly in terms of Rudenko's quadrangular polylogarithms.