Families of automorphic forms
Up till now we have studied individual automorphic forms. These turn out to occur in families in a natural way. For instance, the Poincaré series depends continuously on the weight l, the unitary character x, and the spectral parameter s. The dependence on s is holomorphic. It is not clear from the series that there might be a holomorphic or meromorphic dependence on the character and the weight. In Chapters 9 and 10 we shall get meromorphy by functional analytic methods.
KeywordsParameter Space Open Subset Meromorphic Function Complex Manifold Cusp Form
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