The Dimension of Spaces of Automorphic Forms
نویسنده
چکیده
1. The trace formula of Selberg reduces the problem of calculating the dimension of a space of automorphic forms, at least when there is a compact fundamental domain, to the evaluation of certain integrals. Some of these integrals have been evaluated by Selberg. An apparently different class of definite integrals has occurred in Harish-Chandra’s investigations of the representations of semi-simple groups. These integrals have been evaluated. In this paper, after clarifying the relation between the two types of integrals, we go on to complete the evaluation of the integrals appearing in the trace formula. Before the formula for the dimension that results is described let us review Harish-Chandra’s construction of bounded symmetric domains and introduce the automorphic forms to be considered.
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