Work

A quantitative Selberg’s lemma

Year: 2025

Type: article

Abstract: We show that an arithmetic lattice \Gamma in a semi-simple Lie group G contains a torsion-free subgroup of index \delta(v) where v = \mu (G/\Gamma) is the co-volume of the lattice. We prove that \delta is polynomial in general and poly-logarithmic under the generalized Riemann hypothesis (GRH). We then show that this poly-logarithmic bound is almost optimal, by constructing certain lattices with torsion elements of order {\sim}\frac{\log v}{\log \log v} .

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/865

Authors: Tsachik Gelander, Raz Slutsky

Institutions: Northwestern University, University of Oxford, Weizmann Institute of Science

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408459079

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