On the Goncharov Depth Conjecture and polylogarithms of depth two

Steven Charlton; Herbert Gangl; Danylo Radchenko; Daniil Rudenko

On the Goncharov Depth Conjecture and polylogarithms of depth two

Number Theory 2022-11-11 v2

Authors: Steven Charlton , Herbert Gangl , Danylo Radchenko , Daniil Rudenko

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 $d=2$ .

Keywords

conjectures and proofs

Cite

@article{arxiv.2210.11938,
  title  = {On the Goncharov Depth Conjecture and polylogarithms of depth two},
  author = {Steven Charlton and Herbert Gangl and Danylo Radchenko and Daniil Rudenko},
  journal= {arXiv preprint arXiv:2210.11938},
  year   = {2022}
}

Comments

4 pages, added Corollary 6, title modified to emphasise result on Depth Conjecture

On the Goncharov Depth Conjecture and polylogarithms of depth two

Abstract

Keywords

Cite

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