Poles of L-functions and theta liftings for orthogonal groups

David Ginzburg, Dihua Jiang, David Soudry

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

In this paper, we prove that the first occurrence of global theta liftings from any orthogonal group to either symplectic groups or metaplectic groups can be characterized completely in terms of the location of poles of certain Eisenstein series. This extends the work of Kudla and Rallis and the work of Moeglin to all orthogonal groups. As applications, we obtain results about basic structures of cuspidal automorphic representations and the domain of holomorphy of twisted standard L-functions.

Original languageEnglish (US)
Pages (from-to)693-741
Number of pages49
JournalJournal of the Institute of Mathematics of Jussieu
Volume8
Issue number4
DOIs
StatePublished - Oct 1 2009

Keywords

  • Automorphic forms
  • L-functions
  • Orthogonal groups
  • Periods
  • Theta liftings

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