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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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 | References | Similar Articles | Additional Information

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 $PSL_{2}({\mathbb{R})}$ 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
Email: sj@math.chalmers.se

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01167-9
PII: S 0025-5718(99)01167-9
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