On fourier coefficients of automorphic forms of GL(n)

Dihua Jiang, Baiying Liu

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16 Scopus citations


It is a well-known theorem, due to J. Shalika and I. Piatetski-Shapiro, independently, that any nonzero cuspidal automorphic form on is generic, that is, has a nonzero Whittaker-Fourier coefficient. Its proof follows from the Fourier expansion of the cuspidal automorphic form in terms of its Whittaker-Fourier coefficients. In this paper, we extend this Fourier expansion to the whole discrete spectrum of the space of all square-integrable automorphic forms of and determine the Fourier coefficients of irreducible noncuspidal (residual) automorphic representations of in terms of unipotent orbits.

Original languageEnglish (US)
Pages (from-to)4029-4071
Number of pages43
JournalInternational Mathematics Research Notices
Issue number17
StatePublished - Jan 1 2013

Bibliographical note

Funding Information:
The work of the first named author is supported in part by NSF DMS-1001672.


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