Torsion in maximal arithmetic Fuchsian groups

In this paper, formulas are derived for the number of conjugacy classes of finite cyclic subgroups in a family of arithmetic Fuchsian groups which includes all maximal arithmetic Fuchsian groups. These formulas are given in terms of the arithmetic data which defines the group. Since a formula for the co-area of these groups in similar terms is also known, this means that the signature and hence isomorphism class of any maximal arithmetic Fuchsian group can be completely determined from the arithmetic data defining the group.