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Mathematics of Computation

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On fundamental domains of arithmetic Fuchsian groups

Author: Stefan Johansson
Journal: Math. Comp. 69 (2000), 339-349
MSC (1991): Primary 11F06, 20H10; Secondary 11R52
Published electronically: September 8, 1999
MathSciNet review: 1665958
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Abstract: Let $K$ be a totally real algebraic number field and $\mathcal {O}$ an order in a quaternion algebra $\mathfrak {A}$ over $K$. Assume that the group $\mathcal {O}^1$ of units in $\mathcal {O}$ with reduced norm equal to 1 is embedded into $\mathrm {PSL}_2(\mathbb {R})$ as an arithmetic Fuchsian group. It is shown how Ford’s algorithm can be effectively applied in order to determine a fundamental domain of $\mathcal {O}^1$ as well as a complete system of generators of $\mathcal {O}^1$.

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Additional Information

Stefan Johansson
Affiliation: Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden
Address at time of publication: Department of Mathematics, Institute for Advanced Study, Princeton, NJ 08540

Keywords: Arithmetic Fuchsian groups, quaternion orders, fundamental domains
Received by editor(s): June 4, 1997
Published electronically: September 8, 1999
Article copyright: © Copyright 1999 American Mathematical Society