arXiv subjects
Publications and source records attributed to Herbert Gangl.
This is a short exposition--mostly by way of the toy models ``double logarithm'' and ``triple logarithm''--which should serve as an introduction to a forthcoming article in which we establish a connection between multiple polylogarithms, polygons, trees and algebraic cycles.
We give the first genuine 2-variable functional equation for the 7--logarithm. We investigate and relate identities for the 3-logarithm given by Goncharov and Wojtkowiak and deduce a certain family of functional equations for the 4-logarithm.
For N=5 and N=6, we compute the Voronoi cell complex attached to real N-dimensional quadratic forms, and we obtain the homology of GL_N(Z) with trivial coefficients, up to small primes. We also prove that K_5(Z) = Z and K_6(Z) has only 3-torsion.
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 Kontsevich's original unpublished note is supplied (with his kind permission) in an "Appendix" at the end of the paper.