English

On the functional equations for polylogarithms in one variable

Algebraic Geometry 2015-12-01 v1

Abstract

We develop a new approach to the study of the functional equations satisfied by classical polylogarithms, inspired by Goncharov's conjectures. We prove a sharpened version of Zagier's criterion for such an equation and explain, how our approach leads to a very simple description of the equations in one variable, satisfied by dilogarithm and trilogarithm. Our main result is the complete description of the functional equations for weight four polylogarithm in one variable.

Keywords

Cite

@article{arxiv.1511.09110,
  title  = {On the functional equations for polylogarithms in one variable},
  author = {Daniil Rudenko},
  journal= {arXiv preprint arXiv:1511.09110},
  year   = {2015}
}

Comments

15 pages

R2 v1 2026-06-22T11:56:49.395Z