Polynomial effective density in quotients of H3 and H2× H2

E. Lindenstrauss; A. Mohammadi

doi:10.1007/s00222-022-01162-5

Polynomial effective density in quotients of H³ and H²× H²

E. Lindenstrauss, A. Mohammadi

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL ₂(R) in arithmetic quotients of SL ₂(C) and SL ₂(R) × SL ₂(R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

Original language	English
Pages (from-to)	1141-1237
Number of pages	97
Journal	Inventiones Mathematicae
Volume	231
Issue number	3
DOIs	https://doi.org/10.1007/s00222-022-01162-5
State	Published - Mar 2023

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00222-022-01162-5

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title = "Polynomial effective density in quotients of H3 and H2× H2",

abstract = "We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL 2(R) in arithmetic quotients of SL 2(C) and SL 2(R) × SL 2(R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.",

author = "E. Lindenstrauss and A. Mohammadi",

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AU - Lindenstrauss, E.

AU - Mohammadi, A.

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N2 - We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL 2(R) in arithmetic quotients of SL 2(C) and SL 2(R) × SL 2(R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

AB - We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL 2(R) in arithmetic quotients of SL 2(C) and SL 2(R) × SL 2(R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

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JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

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ER -

Polynomial effective density in quotients of H³ and H²× H²

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