On Poly(ana)logs I

By Philippe Elbaz-Vincent, Herbert Gangl. Compositio Mathematica, 2000

55 citations recorded by the source corpus.

We investigate a connection between the differential of polylogarithms (as considered by Cathelineau) and a finite variant of them. This allows to answer a question raised by Kontsevich concerning the construction of functional equations for the finite analogs, using in part the p-adic version of polylogarithms and recent work of Besser. Kontsevich's original unpublished note is supplied (with his kind permission) in an ‘Appendix’ at the end of the paper.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b1f3b37b8e8a093fb5abc513deb24ce5873d8574

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Congruences for central binomial sums and finite polylogarithms (2010, background): “Some of them are related to functional equations satisfied by the classical polylogarithms (see [9]); a procedure for deducing them from the latter is described in [6].”
The dilogarithm function. (2007, background): “We do not give any further details, referring the reader to the original papers [8] and [14].”
The additive dilogarithm (2002, background): “xp−1,1−x 1,1−x 2/x 1,...,1−xp−1/xp−2,1−a/xp−1) (We take {a} 1 = 1 −a∈P1 −{1}.) To build a class in H0(B(N•))+ and hence in Mone uses that ∂{a}n= {a}n−1 ·{1−a} 1. The following should be compared with [11], where a similar formula is proposed. The key new point here is that algebraic cycles make it p”