Clean Single-Valued Polylogarithms

Charlton, Steven; Duhr, Claude; Gangl, Herbert

Abstract

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 functions. We discuss the basic properties of these functions and, for depths one and two, we present some explicit formulas and results. We also give explicit formulas for the single-valued and clean single-valued version attached to the Nielsen polylogarithms Sn,2(x), and we show how the clean single-valued functions give new evaluations of multiple polylogarithms at certain algebraic points.

Citation

Charlton, S., Duhr, C., & Gangl, H. (2021). Clean Single-Valued Polylogarithms. Symmetry, integrability and geometry: methods and applications, 17, Article 107. https://doi.org/10.3842/SIGMA.2021.107

• Journal Article Type: Article
• Acceptance Date: Nov 28, 2021
• Online Publication Date: Dec 12, 2021
• Publication Date: Jan 1, 2021
• Deposit Date: Mar 6, 2025
• Publicly Available Date: Mar 6, 2025
• Journal: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
• Electronic ISSN: 1815-0659
• Publisher: National Academy of Science of Ukraine
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Article Number: 107
• DOI: https://doi.org/10.3842/SIGMA.2021.107
• Public URL: https://durham-repository.worktribe.com/output/3681349