On Poly(ana)logs I
  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   Kontsevich's original unpublished note is supplied (with his kind permission) in an "Appendix" at the end of the paper. 
Philippe Elbaz-Vincent, Herbert Gangl, Maxim Kontsevich