Functional equations for Rogers dilogarithm

TL;DR

This paper introduces an infinite family of functional equations for the Rogers dilogarithm, showing they all reduce to the well-known 5 terms relation, thus revealing a new structural understanding of these equations.

Contribution

It presents a novel family of functional equations for the Rogers dilogarithm derived from moduli space combinatorics, reducing them all to the 5 terms relation.

Findings

Family of functional equations for Rogers dilogarithm proved

Equations reduce to the 5 terms relation

First such reduction for an infinite family with increasing variables

Abstract

This paper proves a "new" family of functional equations (Eqn) for Rogers dilogarithm. These equations rely on the combinatorics of dihedral coordinates on moduli spaces of curves of genus 0, M 0,n. For n = 4 we find back the duality relation while n = 5 gives back the 5 terms relation. It is then proved that the whole family reduces to the 5 terms relation. In the author's knownledge, it is the first time that an infinite family of functional equations for the dilogarithm with an increasing number of variables (n -- 3 for (Eqn)) is reduced to the 5 terms relation.