On fundamental domains of arithmetic Fuchsian groups

Johansson, Stefan

doi:10.1090/S0025-5718-99-01167-9

On fundamental domains of arithmetic Fuchsian groups
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by Stefan Johansson PDF

Math. Comp. 69 (2000), 339-349 Request permission

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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