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Polylogarithms in Arithmetic and Geometry

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Proceedings of the International Congress of Mathematicians

Abstract

The classical polylogarithms were invented in the correspondence of Leibniz with Bernoulli in 1696 [Lei]. They are defined by the series

$$L{i_n}(z) = \sum\limits_{k = 1}^\infty {\frac{{{z^k}}}{{{k^n}}}} \left| z \right| < 1$$

and continued analytically to a covering of ℂP1\{0,1,∞}:

$$L{i_n}(z): = \int {_0^zL{i_{n - 1}}(t)\frac{{dt}}{t},L{i_1}(z) = - \log (1 - z)}$$

.

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Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Alexander B. Goncharov

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  1. Alexander B. Goncharov
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Editors and Affiliations

  1. Département de Mathématiques, EPFL, 1015, Laussane, Switzerland

    S. D. Chatterji

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© 1995 Birkhäser Verlag, Basel, Switzerland

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Goncharov, A.B. (1995). Polylogarithms in Arithmetic and Geometry. In: Chatterji, S.D. (eds) Proceedings of the International Congress of Mathematicians. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9078-6_31

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  • DOI: https://doi.org/10.1007/978-3-0348-9078-6_31

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9897-3

  • Online ISBN: 978-3-0348-9078-6

  • eBook Packages: Springer Book Archive

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