Arithmetic Fuchsian groups of genus zero

Darren Long, Colin MacLachlan, Alan Reid

Research output: Contribution to journalArticle

Abstract

If ¡ is a finite co-area Fuchsian group acting on H2, then the quotient H2=¡ is a
hyperbolic 2-orbifold, with underlying space an orientable surface (possibly with
punctures) and a finite number of cone points. Through their close connections
with number theory and the theory of automorphic forms, arithmetic Fuchsian
groups form a widely studied and interesting subclass of finite co-area Fuchsian
groups. This paper is concerned with the distribution of arithmetic Fuchsian
groups ¡ for which the underlying surface of the orbifold H2=¡ is of genus zero;
for short we say ¡ is of genus zero.
Original languageEnglish
Pages (from-to)569-599
JournalPure and Applied Mathematical Quarterly
Volume2
Issue number2
Publication statusPublished - Apr 2006

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Arithmetic Groups
Fuchsian Group
Genus
Orbifold
Zero
Automorphic Forms
Number theory
Quotient
Cone

Keywords

  • rational homology
  • modular group
  • fields
  • subgroups
  • curves
  • forms

Cite this

Long, D., MacLachlan, C., & Reid, A. (2006). Arithmetic Fuchsian groups of genus zero. Pure and Applied Mathematical Quarterly, 2(2), 569-599.

Arithmetic Fuchsian groups of genus zero. / Long, Darren; MacLachlan, Colin; Reid, Alan.

In: Pure and Applied Mathematical Quarterly, Vol. 2, No. 2, 04.2006, p. 569-599.

Research output: Contribution to journalArticle

Long, D, MacLachlan, C & Reid, A 2006, 'Arithmetic Fuchsian groups of genus zero', Pure and Applied Mathematical Quarterly, vol. 2, no. 2, pp. 569-599.
Long D, MacLachlan C, Reid A. Arithmetic Fuchsian groups of genus zero. Pure and Applied Mathematical Quarterly. 2006 Apr;2(2):569-599.
Long, Darren ; MacLachlan, Colin ; Reid, Alan. / Arithmetic Fuchsian groups of genus zero. In: Pure and Applied Mathematical Quarterly. 2006 ; Vol. 2, No. 2. pp. 569-599.
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