Automorphic Forms, Cohomology and CAP Representations. The Case $GL_2$ over a definite quaternion algebra

Abstract

In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group G = GL 2 over a definite quaternion algebra D/Q. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree 1. The latter ones turn out to be CAPrepresentations, though G satisfies Strong Multiplicity One. A non-vanishing result on intertwining operators of induced representations will serve as a starting point for further investigations concerning rationality of critical L-values.