Magee, Michael (2015) 'Quantitative spectral gap for thin groups of hyperbolic isometries.', Journal of the European Mathematical Society., 17 (1). pp. 151-187.
Let ΛΛ be a subgroup of an arithmetic lattice in SO(n+1,1)SO(n+1,1). The quotient Hn+1/ΛHn+1/Λ has a natural family of congruence covers corresponding to ideals in a ring of integers. We establish a super-strong approximation result for Zariski-dense ΛΛ with some additional regularity and thickness properties. Concretely, this asserts a quantitative spectral gap for the Laplacian operators on the congruence covers. This generalizes results of Sarnak and Xue (1991) and Gamburd (2002).
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.4171/JEMS/500|
|Date accepted:||No date available|
|Date deposited:||24 October 2017|
|Date of first online publication:||05 February 2015|
|Date first made open access:||24 October 2017|
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