### Abstract

Original language | English |
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Pages (from-to) | 111-123 |

Number of pages | 13 |

Journal | Bulletin of the London Mathematical Society |

Volume | 43 |

Issue number | 1 |

Early online date | 2 Nov 2010 |

DOIs | |

Publication status | Published - Feb 2011 |

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### Cite this

*Bulletin of the London Mathematical Society*,

*43*(1), 111-123. https://doi.org/10.1112/blms/bdq085

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

Research output: Contribution to journal › Article

*Bulletin of the London Mathematical Society*, vol. 43, no. 1, pp. 111-123. https://doi.org/10.1112/blms/bdq085

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TY - JOUR

T1 - Bounds for discrete hyperbolic arithmetic reflection groups in dimension 2

AU - MacLachlan, Colin

PY - 2011/2

Y1 - 2011/2

N2 - 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.

AB - 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.

U2 - 10.1112/blms/bdq085

DO - 10.1112/blms/bdq085

M3 - Article

VL - 43

SP - 111

EP - 123

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 1

ER -