On Whittaker models and the vanishing of Fourier coefficients of cusp forms
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The purpose of this paper is to construct examples of automorphic cuspidal representations which possess a ψ-Whittaker model even though their ψ-Fourier coefficients vanish identically. This phenomenon was known to be impossible for the groupGL(n), but in general remained an open problem. Our examples concern the metaplectic group and rely heavily upon J L Waldspurger’s earlier analysis of cusp forms on this group.
KeywordsWhittaker models cusp forms automorphic cuspidal representations
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