The density hypothesis for horizontal families of lattices

Abstract

We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving bounds on the multiplicities of non-tempered representations are uniform in the volume and spectral aspects.

arXiv comment34 pages, LaTeX2e

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• Limit multiplicities for principal congruence subgroups of GL(n) and SL(n)
• Applications of analytic newvectors for $\mathrm{GL}(n)$
• Strong Limit Multiplicity for arithmetic hyperbolic surfaces and $3$-manifolds
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Cited by in corpus (1)

• Beyond the spherical sup-norm problem