Finite polylogarithms, their multiple analogues and the Shannon entropy

28/10/2015
Publication GSI2015
OAI : oai:www.see.asso.fr:11784:14285

Résumé

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.

Finite polylogarithms, their multiple analogues and the Shannon entropy

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application/pdf Finite polylogarithms, their multiple analogues and the Shannon entropy Philippe Elbaz-Vincent, Herbert Gangl
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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.
Finite polylogarithms, their multiple analogues and the Shannon entropy

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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.

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