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On the Goncharov Depth Conjecture and polylogarithms of depth two

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arxiv 2210.11938 v2 pith:VLZGY6HX submitted 2022-10-21 math.NT

Steven Charlton , Herbert Gangl , Danylo Radchenko , Daniil Rudenko This is my paper · ORCID
classification math.NT
keywords depthconjecturedotsgoncharovpolylogarithmsproveexpressedfunction
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We prove the surjectivity part of Goncharov's depth conjecture. We also show that the depth conjecture implies that multiple polylogarithms of depth $d$ and weight $n$ can be expressed via a single function $\mathrm{Li}_{n-d+1,1,\dots,1}(a_1,a_2,\dots,a_d)$, and we prove this latter statement for $d=2$.

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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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