Exceptional eigenvalue density for thin groups

Christopher Lutsko

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arXiv · 2608.18236

Exceptional eigenvalue density for thin groups

Christopher Lutsko

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Abstract

We prove a limit multiplicity conjecture of Hee Oh for principal congruence covers of geometrically finite hyperbolic manifolds, with an explicit power-saving rate. The rate is governed by the return of Patterson--Sullivan shadows through a fixed compact core, giving a geometric interpretation to the exceptional eigenvalue density. For convex-cocompact groups, a packing argument for enlarged shadows gives a stronger rate.

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Christopher Lutsko. 2026-08-18. Exceptional eigenvalue density for thin groups. https://arxiv.org/abs/2608.18236

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