6 citations · 25 across the 19 of their papers we have counts for
21 papers
A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz
Steven Charlton, Bernhard Heim, Markus Neuhauser +2
Heretofore, the second and third author conjectured that the D'Arcais polynomials, related to the coefficients of the powers of the Dedekind -function, are Hurwitz polynomials e…
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,…
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…
Evaluation of the multiple zeta values and period polynomial relations
Steven Charlton, Adam Keilthy
In studying the depth filtration on multiple zeta values, difficulties quickly arise due to a disparity between it and the coradical filtration. In particular, there are additional…
Symmetry results for multiple -values
Steven Charlton, Michael E. Hoffman
For a composition whose first part exceeds 1, we can define the multiple -value as the sum of all the terms in the series for the multiple zeta value whose den…
On the evaluation of the alternating multiple value
Steven Charlton
We prove an evaluation for the stuffle-regularised multiple value in terms of , and . This…
On motivic multiple values, Saha's basis conjecture, and generators of alternating MZV's
Steven Charlton
We give an evaluation for the stuffle-regularised as a polynomial in single-zeta values, and . We then apply this to establish some lin…
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…
Generalized Jacobi-Trudi determinants and evaluations of Schur multiple zeta values
Henrik Bachmann, Steven Charlton
We present new determinant expressions for regularized Schur multiple zeta values. These generalize the known Jacobi-Trudi formulae and can be used to quickly evaluate certain type…
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…
Analogues of cyclic insertion type identities for multiple zeta star values
Steven Charlton
We prove an identity for multiple zeta star values, which generalises some identities due to Imatomi, Tanaka, Tasaka and Wakabayashi. This identity gives an analogue of cyclic inse…
The alternating block decomposition of iterated integrals, and cyclic insertion on multiple zeta values
Steven Charlton
The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lisoněk states that by inserting all cyclic permutations of some initial blocks of 2's into the multiple zeta va…
A review of Dan's reduction method for multiple polylogarithms
Steven Charlton
In this paper we will give an account of Dan's reduction method for reducing the weight multiple logarithm to an explicit sum of l…
ζ({{2}^m, 1, {2}^m, 3}^n, {2}^m) / π^{4n + 2m(2n+1)} is rational
Steven Charlton
The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lisoněk states that inserting all cyclic shifts of some fixed blocks of 2's into the multiple zeta value ζ(1,3,.…