Arithmetic Fuchsian groups of genus zero

Darren Long, Colin MacLachlan, Alan Reid

Research output: Contribution to journalArticlepeer-review


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
Issue number2
Publication statusPublished - Apr 2006


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


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