| Résume | The polylogarithm is a very successful tool in the study ofspecial values of L-functions. So far, only the polylogarithmon the multiplicative group and on elliptic curves were subjectof deeper investigation. In this talk we will consider the polylogarithmon modular curves and establish some of its properties.We show in particular, that its periods are given by Goncharov'spolylogarithmic functions, which are described in terms of Greenfunctions, and showthat the dilogarithm is related to the L-value at 2 of a cuspform of weight 2 (this depends on calculations by Brunaultin his thesis). Moreover, we show that one gets in a natural wayan Euler system for the Galois representation associated tosuch a cusp form. In the last part of the lecture we discuss workin progress about relations of the modular polylog to Kato's Eulersystem and the elliptic Zagier conjecture. |
