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 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |