HARMONIC-ANALYSIS IN WEIGHTED L-2-SPACES

In this article, we prove a conjecture of Borel, which states that the inclusion of the space of automorphic forms into the space of all C-i nfinity-functions induces an isomorphism on the cohomology with coeffi cients in a finite-dimensional representation. We also prove that ever y automorphic form is a sum of derivatives of Eisenstein series and ap ply these results to the generalisation of the Manin-Drinfeld theorem and to the trace formula for Hecke operators.