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arXiv · 1706.02180

Counting non-uniform lattices

Mikhail Belolipetsky·Alex Lubotzky
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Abstract

In [BGLM] and [GLNP] it was conjectured that if $H$ is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices in $H$ of covolume at most $x$ is $x^{(\gamma(H)+o(1))\log x/\log\log x}$ where $\gamma(H)$ is an explicit constant computable from the (absolute) root system of $H$. In [BLu] we disproved this conjecture. In this paper we prove that for most groups $H$ the conjecture is actually true if we restrict to counting only non-uniform lattices.

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Mikhail Belolipetsky, Alex Lubotzky. 2017-06-06. Counting non-uniform lattices. https://arxiv.org/abs/1706.02180

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