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arXiv · 2210.11938

On the Goncharov Depth Conjecture and polylogarithms of depth two

Steven Charlton·Herbert Gangl·Danylo Radchenko·Daniil Rudenko
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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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Steven Charlton, Herbert Gangl, Danylo Radchenko, Daniil Rudenko. 2022-10-21. On the Goncharov Depth Conjecture and polylogarithms of depth two. https://arxiv.org/abs/2210.11938

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