Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Volume 2013, Issue 11, Pages 2601-2623Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rns139
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Funding
- National Science Foundation [DMS-0635607]
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We use the theta lift to study the multiplicity with which certain automorphic representations of cohomological type occur in a family of congruence covers of an arithmetic manifold. When the family of covers is a so-called p-adic congruence tower, we obtain sharp asymptotics for the number of representations that occur as lifts. When combined with theorems on the surjectivity of the theta lift due to Howe and Li, and Bergeron, Millson, and Moeglin, this allows us to verify certain cases of a conjecture of Sarnak and Xue.
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