Finite polylogarithms, their multiple analogues and the Shannon entropy

28/10/2015
Publication GSI2015
OAI : oai:www.see.asso.fr:11784:14285
DOI : http://dx.doi.org/10.1007/978-3-319-25040-3_31You do not have permission to access embedded form.

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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        <identifier identifierType="DOI">10.23723/11784/14285</identifier><creators><creator><creatorName>Philippe Elbaz-Vincent</creatorName></creator><creator><creatorName>Herbert Gangl</creatorName></creator></creators><titles>
            <title>Finite polylogarithms, their multiple analogues and the Shannon entropy</title></titles>
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        <publicationYear>2015</publicationYear>
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	    <date dateType="Created">Sun 8 Nov 2015</date>
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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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