289 citations · 330 across the 18 of their papers we have counts for
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On the Goncharov Depth Conjecture and polylogarithms of depth two
Steven Charlton, Herbert Gangl, Danylo Radchenko +1
We prove the surjectivity part of Goncharov's depth conjecture. We also show that the depth conjecture implies that multiple polylogarithms of depth and weight can be expre…
On two conjectures of Sun concerning Apéry-like series
Steven Charlton, Herbert Gangl, Li Lai +2
In this paper, we shall prove two conjectures of Z.-W. Sun concerning Apéry-like series. One of the series is alternating whereas the other one is not. Our main strategy is to conv…
Clean Single-Valued Polylogarithms
Steven Charlton, Claude Duhr, Herbert Gangl
We define a variant of real-analytic polylogarithms that are single-valued and that satisfy ''clean'' functional relations that do not involve any products of lower weight function…
Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7
Steven Charlton, Herbert Gangl, Danylo Radchenko
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 $\m…
Explicit formulas for Grassmannian polylogarithms
Steven Charlton, Herbert Gangl, Danylo Radchenko
We give new explicit formulas for Grassmannian and Aomoto polylogarithms in terms of iterated integrals, for arbitrary weight. We also explicitly reduce the Grassmannian polylogari…
On functional equations for Nielsen polylogarithms
Steven Charlton, Herbert Gangl, Danylo Radchenko
We derive new functional equations for Nielsen polylogarithms. We show that, when viewed modulo and products of lower weight functions, the weight Nielsen polyl…