Mathematische Zeitschrift

, Volume 273, Issue 1–2, pp 173–210 | Cite as

Canonical models of arithmetic (1; e)-curves

  • Jeroen Sijsling


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.


Shimura curves Arithmetic groups Uniformization Explicit methods 

Mathematics Subject Classification (2010)

Primary 11G18 Secondary 14G35 14Q05 


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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands
  2. 2.IRMARRennesFrance

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