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^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

4 Scopus citations

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

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© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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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.",

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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.

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Polynomial effective density in quotients of H³ and H²× H²

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