On fundamental domains of arithmetic Fuchsian groups
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- by Stefan Johansson;
- Math. Comp. 69 (2000), 339-349
- DOI: https://doi.org/10.1090/S0025-5718-99-01167-9
- Published electronically: September 8, 1999
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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 $\mathcal {O}^1$.References
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Bibliographic 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
- Received by editor(s): June 4, 1997
- Published electronically: September 8, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 339-349
- MSC (1991): Primary 11F06, 20H10; Secondary 11R52
- DOI: https://doi.org/10.1090/S0025-5718-99-01167-9
- MathSciNet review: 1665958