On the genericity of cuspidal automorphic forms of SO(2n+1), II

Dihua Jiang, David Soudry

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Abstract

This paper is a continuation of our previous work (D. Jiang and D. Soudry, On the genericity of cuspidal automorphic forms on SO2n+1, J. reine angew. Math., to appear). We extend Moeglin's results (C. Moeglin, J. Lie Theory 7 (1997), 201-229, 231-238) from the even orthogonal groups to old orthogonal groups and complete our proof of the CAP conjecture for irreducible cuspidal automorphic representations of SO2n+1(double-struck A sign) with special Bessel models. We also give a characterization of the vanishing of the central value of the standard L-function of SO2n+1 (double-struck A sign) in terms of theta correspondence. As a result, we obtain the weak Langlands functorial transfer from SO2n+1(double-struck A sign) to GL2n(double-struck A sign) for irreducible cuspidal automorphic representations of SO2n+1(double-struck A sign) with special Bessel models.

Original languageEnglish (US)
Pages (from-to)721-748
Number of pages28
JournalCompositio Mathematica
Volume143
Issue number3
DOIs
StatePublished - May 2007

Keywords

  • Cuspidal automorphic forms
  • Langlands functoriality

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