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)|
|Number of pages||49|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|State||Published - Oct 1 2009|
- Automorphic forms
- Orthogonal groups
- Theta liftings