Counting non-uniform lattices

Mikhail Belolipetsky; Alexander Lubotzky

doi:10.1007/s11856-019-1868-4

Counting non-uniform lattices

Mikhail Belolipetsky, Alexander Lubotzky

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

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^{(γ(H)+o(1)) log x/ log log x} where γ(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.

Original language	English
Pages (from-to)	201-229
Number of pages	29
Journal	Israel Journal of Mathematics
Volume	232
Issue number	1
DOIs	https://doi.org/10.1007/s11856-019-1868-4
State	Published - 1 Aug 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-019-1868-4

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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(γ(H)+o(1)) log x/ log log x where γ(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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AB - 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(γ(H)+o(1)) log x/ log log x where γ(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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VL - 232

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EP - 229

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Counting non-uniform lattices

Abstract

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