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Finite Polylogarithms, Their Multiple Analogues and the Shannon Entropy

  • Philippe Elbaz-VincentEmail author
  • Herbert Gangl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)

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.

Keywords

Finite Field Shannon Entropy Entropy Function Multiple Polylogarithms Formal Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut FourierCNRS-Université Grenoble AlpesSaint Martin D’hèresFrance
  2. 2.Department of Mathematical SciencesUniversity of DurhamDurhamUK

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