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Poles of L-functions and theta liftings for orthogonal groups

Part of: Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  10 June 2009

David Ginzburg ,
Dihua Jiang  and
David Soudry
David Ginzburg
Affiliation:
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (ginzburg@post.tau.ac.il; soudry@post.tau.ac.il)
Dihua Jiang
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA (dhjiang@math.umn.edu
David Soudry
Affiliation:
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (ginzburg@post.tau.ac.il; soudry@post.tau.ac.il)
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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.

Keywords

orthogonal groupstheta liftingsautomorphic formsL-functionsperiods

MSC classification

Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 4 , October 2009 , pp. 693 - 741
Copyright
Copyright © Cambridge University Press 2009

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