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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

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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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. 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.