Bounds for discrete hyperbolic arithmetic reflection groups in dimension 2

Colin MacLachlan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Here we show that if G is an arithmetic Fuchsian group of genus 0, then the totally real defining field k of G must be such that [k : Q] = 11. The same inequality holds for discrete arithmetic hyperbolic reflection groups acting on a two-dimensional hyperbolic space H2. In addition, we show that there exists an arithmetic Fuchsian group of genus 0 containing an element of order N if and only if N ¿ {2, 3, …, 16, 18, 20, 22, 24, 26, 28, 30, 36}. A slightly less precise statement holds for discrete arithmetic hyperbolic reflection groups acting on H2.
Original languageEnglish
Pages (from-to)111-123
Number of pages13
JournalBulletin of the London Mathematical Society
Volume43
Issue number1
Early online date2 Nov 2010
DOIs
Publication statusPublished - Feb 2011

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Arithmetic Groups
Fuchsian Group
Hyperbolic Groups
Reflection Group
Genus
Hyperbolic Space
If and only if

Cite this

Bounds for discrete hyperbolic arithmetic reflection groups in dimension 2. / MacLachlan, Colin.

In: Bulletin of the London Mathematical Society, Vol. 43, No. 1, 02.2011, p. 111-123.

Research output: Contribution to journalArticle

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