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.
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