English

Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7

Number Theory 2020-12-18 v1

Abstract

We present new functional equations in weights 5, 6 and 7 and use them for explicit depth reduction of multiple polylogarithms. These identities generalize the crucial identity Q4\mathbf{Q}_4 from the recent work of Goncharov and Rudenko that was used in their proof of the weight 4 case of Zagier's Polylogarithm Conjecture.

Keywords

Cite

@article{arxiv.2012.09840,
  title  = {Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7},
  author = {Steven Charlton and Herbert Gangl and Danylo Radchenko},
  journal= {arXiv preprint arXiv:2012.09840},
  year   = {2020}
}

Comments

6 pages, 4 figures

R2 v1 2026-06-23T21:03:33.826Z