Arithmetic Fuchsian groups of genus zero

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.