Finite polylogarithms, their multiple analogues and the Shannon entropy

Philippe Elbaz-Vincent (1) , Herbert Gangl (2)

1 IF - Institut Fourier
2 Department of Mathematical Sciences, University of Durham

We show that the entropy function—and hence the finite 1-logarithm—behaves a lot like certain derivations. We recall its coho-mological 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.

Mots clés: cohomological interpretation of Shannon entropy; number theoretic applications of finite multiple polylogarithms; functional equations of multiple polylogarithms; finite polylogarithms; information theory; Shannon entropy

Domaines: Théorie des nombres [math.NT]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Philippe Elbaz-Vincent, Herbert Gangl. Finite polylogarithms, their multiple analogues and the Shannon entropy. Geometric Science of Information 2015, Oct 2015, Palaiseau, France. ⟨hal-01176710⟩