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theta liftings

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

Poles of L-functions and theta liftings for orthogonal groups
Part of
- Discontinuous groups and automorphic forms
- Lie groups
David Ginzburg, Dihua Jiang, David Soudry
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 8 / Issue 4 / October 2009

Published online by Cambridge University Press:

10 June 2009, pp. 693-741

Print publication:

October 2009
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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.