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

Steven Charlton, Herbert Gangl, Danylo Radchenko

Published 2020-12-17Version 1

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 $\mathbf{Q}_4$ from the recent work of Goncharov and Rudenko that was used in their proof of the weight 4 case of Zagier's Polylogarithm Conjecture.