Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative spectral gap for thin groups of hyperbolic isometries   Let $\Lambda$ be a subgroup of an arithmetic lattice in SO(n+1,1). The
quotient $\mathbb{H}^{n+1} / \Lambda$ has a natural family of congruence covers
corresponding to primes in some ring of integers. We establish a super-strong
approximation result for Zariski-dense $\Lambda$ 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).

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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin