Theta lifting and cohomology growth in p-adic towers

Details Theta lifting and cohomology growth in p-adic towers Theta lifting and cohomology growth in p-adic towers

2011-06-14

arxiv.org/abs/1106.2765v3

Mathematics

Number Theory

17 pages

Scientific paper

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 which 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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