Canonical models of arithmetic (1; e)-curves


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).

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  • Shimura curves
  • Arithmetic groups
  • Uniformization
  • Explicit methods

Mathematics Subject Classification (2010)

  • Primary 11G18
  • Secondary 14G35
  • 14Q05