ON EULER PRODUCTS AND RESIDUAL EISENSTEIN COHOMOLOGY CLASSES FOR SIEGEL MODULAR VARIETIES

In the case of the symplectic similitude group G = GSp2 defined over Q it is studied which contribution to the cohomology of arithmetic subgroups of G is given by the residual spectrum of G. This is done in the broader context of giving a description of the cohomology 'at infinity' in terms of Eisenstein series or residues of such. It is shown how the structure of the space spanned by Eisenstein cohomology classes is related to the analytic properties of certain Euler products attached to cuspidal automorphic representations of GL2.