On fundamental domains of arithmetic Fuchsian groups

Journal article, 2000

Let K be a totally real algebraic number field and O an order in a quaternion algebra A over K. Assume that the group O^1 of units in O with reduced norm equal to 1 is embedded into PSL_{2}(R) as an arithmetic Fuchsian group. It is shown how Ford's algorithm can be effectively applied in order to determine a fundamental domain of O^1 as well as a complete system of generators of O^1.