Clean Single-Valued Polylogarithms
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211420 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Clean Single-Valued Polylogarithms. Steven Charlton, Claude Duhr and Herbert Gangl. SIGMA 17 (2021), 107, 34 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862741153247395840 |
|---|---|
| author | Charlton, Steven Duhr, Claude Gangl, Herbert |
| author_facet | Charlton, Steven Duhr, Claude Gangl, Herbert |
| citation_txt | Clean Single-Valued Polylogarithms. Steven Charlton, Claude Duhr and Herbert Gangl. SIGMA 17 (2021), 107, 34 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 ₙ‚₂(), and we show how the clean single-valued functions give new evaluations of multiple polylogarithms at certain algebraic points.
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| first_indexed | 2026-04-17T17:53:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211420 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T17:53:15Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Charlton, Steven Duhr, Claude Gangl, Herbert 2026-01-02T08:29:12Z 2021 Clean Single-Valued Polylogarithms. Steven Charlton, Claude Duhr and Herbert Gangl. SIGMA 17 (2021), 107, 34 pages 1815-0659 2020 Mathematics Subject Classification: 11G55; 11M32; 33E20; 39B32 arXiv:2104.04344 https://nasplib.isofts.kiev.ua/handle/123456789/211420 https://doi.org/10.3842/SIGMA.2021.107 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 ₙ‚₂(), and we show how the clean single-valued functions give new evaluations of multiple polylogarithms at certain algebraic points. We 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Clean Single-Valued Polylogarithms Article published earlier |
| spellingShingle | Clean Single-Valued Polylogarithms Charlton, Steven Duhr, Claude Gangl, Herbert |
| title | Clean Single-Valued Polylogarithms |
| title_full | Clean Single-Valued Polylogarithms |
| title_fullStr | Clean Single-Valued Polylogarithms |
| title_full_unstemmed | Clean Single-Valued Polylogarithms |
| title_short | Clean Single-Valued Polylogarithms |
| title_sort | clean single-valued polylogarithms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211420 |
| work_keys_str_mv | AT charltonsteven cleansinglevaluedpolylogarithms AT duhrclaude cleansinglevaluedpolylogarithms AT ganglherbert cleansinglevaluedpolylogarithms |