5 papers
On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials
Steven Charlton, Bernhard Heim, Johann Stumpenhusen
Recently, Starr used asymptotic methods to disprove a conjecture by Heim--Neuhauser and Abdesselam about the log-concavity of the D'Arcais polynomials, without giving an explicit c…
Multiple zeta values ending with a fixed string
Steven Charlton
We give a generating series expression for the sum of all multiple zeta values of a fixed weight, depth, and height, which end with a given string $\vec{\ell} = (\ell_1,\ldots,\ell…
Multiple polylogarithms and the Steinberg module
Steven Charlton, Danylo Radchenko, Daniil Rudenko
We establish a connection between multiple polylogarithms on a torus and the Steinberg module of , and show that multiple polylogarithms of depth and weight can…
The Hopf algebra of formal multiple polylogarithms
Steven Charlton, Andrei Matveiakin, Danylo Radchenko +1
We define a Hopf algebra of polylogarithms of an arbitrary field, which is a candidate for a conjectural Hopf algebra of framed mixed Tate motives. Our definition is elementary and…
Symmetries of weight 6 multiple polylogarithms and Goncharov's Depth Conjecture
Steven Charlton
We prove that the weight 6, depth 3, multiple polylogarithm , or rather its more natural `divergent' incarnation $ \mathrm{Li}_{3;1,1,1}(x,…