Clean Single-Valued Polylogarithms

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dc.contributor.authorCharlton, Steven
dc.contributor.authorDuhr, Claude
dc.contributor.authorGangl, Herbert
dc.date.accessioned2026-01-02T08:29:12Z
dc.date.issued2021
dc.description.abstractWe 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.
dc.description.sponsorshipWe are grateful to Falko Dulat for early collaboration on this project. We would like to thank the MITP in Mainz, where this work was started, and the HIM in Bonn and the GGI in Florence for the hospitality where part of this work was developed. We are particularly grateful to the organisers of the workshop on “Modular forms, periods and scattering amplitudes” at the ETH Zürich in April 2019, where some of our results were first presented. In particular, we are grateful to Francis Brown and Erik Panzer for pointing out the relevance of the Dynkin operator in the construction of the clean single-valued analogues of multiple polylogarithms. SC is grateful to the Max-Planck-Institut f¨ur Mathematik in Bonn for support, hospitality, and excellent working conditions during his stay, where some of this work was undertaken. SC was also partially supported by DFG Eigene Stelle grant CH 2561/1-1, for Projektnummer 442093436.
dc.identifier.citationClean Single-Valued Polylogarithms. Steven Charlton, Claude Duhr and Herbert Gangl. SIGMA 17 (2021), 107, 34 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2021.107
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 11G55; 11M32; 33E20; 39B32
dc.identifier.otherarXiv:2104.04344
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211420
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleClean Single-Valued Polylogarithms
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2021, том 17, випуск за цей рік