Poles of L-functions and theta liftings for orthogonal groups

David Ginzburg; Dihua Jiang; David Soudry

doi:10.1017/S1474748009000097

Poles of L-functions and theta liftings for orthogonal groups

David Ginzburg, Dihua Jiang, David Soudry

School of Mathematics

Research output: Contribution to journal › Article › peer-review

20 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 language	English (US)
Pages (from-to)	693-741
Number of pages	49
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	8
Issue number	4
DOIs	https://doi.org/10.1017/S1474748009000097
State	Published - Oct 2009

Bibliographical note

Funding Information:
Acknowledgements. The research of D. J. is supported in part by NSF grant DMS-0400414 and by NSF grant DMS-0653742 and also by the Chinese Academy of Sciences. All three authors are partially supported by the USA–Israel Binational Science Foundation.

Keywords

Automorphic forms
L-functions
Orthogonal groups
Periods
Theta liftings

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10.1017/S1474748009000097

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AU - Jiang, Dihua

AU - Soudry, David

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N2 - 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.

AB - 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.

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KW - L-functions

KW - Orthogonal groups

KW - Periods

KW - Theta liftings

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Poles of L-functions and theta liftings for orthogonal groups

Abstract

Bibliographical note

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