Abstract

The main theme of this paper is that singular automorphic forms on classical groups are given by theta series liftings. We establish several inequalities relating the automorphic multiplicities of a given representation and that of its abstract theta lift. Our methods allow one to lift noncuspidal, square integrable automorphic forms when the dual pair involved is in the stable range. In this way we construct new families of singular automorphic forms, many of which are clearly unipotent. In fact, starting from one-dimensional representations and repeating the procedure (of lifting in the stable range), one may obtain all automorphic forms which are quadratic unipotent in the sense of Moeglin.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 523-578
Launched on MUSE
1997-06-01
Open Access
No
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