On Whittaker models and the vanishing of Fourier coefficients of cusp forms

Stephen Gelbart; David Soudry

doi:10.1007/BF02837815

On Whittaker models and the vanishing of Fourier coefficients of cusp forms

Stephen Gelbart^*, David Soudry

^*Corresponding author for this work

School of Mathematical Sciences

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

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Abstract

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 group GL(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.

Original language	English
Pages (from-to)	67-74
Number of pages	8
Journal	Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume	97
Issue number	1-3
DOIs	https://doi.org/10.1007/BF02837815
State	Published - Dec 1987

Keywords

Whittaker models
automorphic cuspidal representations
cusp forms

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10.1007/BF02837815

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On Whittaker models and the vanishing of Fourier coefficients of cusp forms

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Keywords

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