On fourier coefficients of automorphic forms of GL(n)

Dihua Jiang, Baiying Liu

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

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
Volume2013
Issue number17
DOIs
StatePublished - Sep 4 2013

Fingerprint Dive into the research topics of 'On fourier coefficients of automorphic forms of GL(n)'. Together they form a unique fingerprint.

Cite this