Abstract
The Fuchsian groups of signature (1; e) are the simplest class of Fuchsian groups for which the calculation of the corresponding quotient of the upper half plane presents a challenge. This paper considers the finite list of arithmetic (1; e)-groups. We define canonical models for the associated quotients by relating these to genus 1 Shimura curves. These models are then calculated by applying results on the \({\mathfrak{p}}\)-adic uniformization of Shimura curves and Hilbert modular forms.
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Sijsling, J. Canonical models of arithmetic (1; e)-curves. Math. Z. 273, 173–210 (2013). https://doi.org/10.1007/s00209-012-1000-5
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DOI: https://doi.org/10.1007/s00209-012-1000-5