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Cluster Polylogarithms I: Quadrangular Polylogarithms

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

Andrei Matveiakin , Daniil Rudenko This is my paper · ORCID
classification math.AGmath.NT
keywords polylogarithmsclusterarbitraryequationsgoncharovweightabelapplication
verification ladder T0 review T1 audit T2 compute T3 formal
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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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  1. The Hopf algebra of formal multiple polylogarithms

    math.NT 2024-11 conditional novelty 6.0 of 10

    A new Hopf algebra of formal multiple polylogarithms is defined for every field, with Hodge and motivic realizations, proposed as the conjectural Hopf algebra of framed mixed Tate motives.

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