Describing all multivariable functional equations of dilogarithms (2007.11014v1)

Abstract: We prove quite general statements about functional equations in any number of variables for the dilogarithms defined by Bloch-Wigner, Rogers, and Coleman, showing that they follow from certain 5-term and 2-term relations in a precise way. Unlike many other references, we use arbitrary coefficients, do not ignore any torsion, and get sharp results. For the Bloch-Wigner dilogarithm, we also consider complex conjugation, and for Coleman's p-adic dilogarithm we show independence of the branch.