Fourier-Jacobi expansion of automorphic forms on Sp (1, q) generating quaternionic discrete series

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Abstract

The aim of this paper is to develop the notion of the Fourier expansion of automorphic forms on Sp (1, q) generating quaternionic discrete series, which are non-holomorphic forms. There is such an expansion given by Tsuneo Arakawa, assuming the boundedness of the forms and the integrability of the discrete series. We study these automorphic forms without such assumptions. When q > 1 we prove the "Koecher principle" for such automorphic forms, whose validity is known for holomorphic automorphic forms except elliptic modular forms.

Original languageEnglish
Pages (from-to)638-682
Number of pages45
JournalJournal of Functional Analysis
Volume239
Issue number2
DOIs
Publication statusPublished - 2006 Oct 15

Keywords

  • Fourier expansion
  • Generalized Whittaker functions
  • Koecher principle
  • Quaternionic discrete series
  • The real symplectic group of signature (1 +, q -)

ASJC Scopus subject areas

  • Analysis

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