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Finite polylogarithms, their multiple analogues and the Shannon entropy


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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Finite polylogarithms, their multiple analogues and the Shannon entropy
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