Some new results on the Eichler cohomology of automorphic forms

Abstract

We here formulate and prove several new results concerning the Eichler cohomology of automorphic forms on finitely generated Fuchsian groups of the first kind and, in particular, on //-groups. The Eichler cohomology we introduce is connected with automorphic forms of arbitrary real degree (as opposed to integral degree), with a suitably chosen underlying space of functions analytic in the upper half-plane. We obtain structure theorems for the Eichler cohomology groups which are analogous to earlier results of Eichler and Gunning.