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Finite Polylogarithms, Their Multiple Analogues and the Shannon Entropy

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Geometric Science of Information (GSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

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Abstract

We show that the entropy function—and hence the finite 1-logarithm—behaves a lot like certain derivations. We recall its cohomological interpretation as a 2-cocycle and also deduce 2n-cocycles for any n. Finally, we give some identities for finite multiple polylogarithms together with number theoretic applications.

Partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01) and by the LabEx AMIES.

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Acknowledgement

We would like to express our sincere gratitude to the reviewers for their valuable comments who have helped improve this paper

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Authors and Affiliations

  1. Institut Fourier, CNRS-Université Grenoble Alpes, BP 74, 38402, Saint Martin D’hères, France

    Philippe Elbaz-Vincent

  2. Department of Mathematical Sciences, University of Durham, South Road, Durham, UK

    Herbert Gangl

Authors
  1. Philippe Elbaz-Vincent
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  2. Herbert Gangl
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Corresponding author

Correspondence to Philippe Elbaz-Vincent .

Editor information

Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Elbaz-Vincent, P., Gangl, H. (2015). Finite Polylogarithms, Their Multiple Analogues and the Shannon Entropy. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_31

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

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