Modular Curves as Riemann Surfaces

  • Fred Diamond
  • Jerry Shurman
Part of the Graduate Texts in Mathematics book series (GTM, volume 228)


For any congruence subgroup \(\Gamma\) of \(\mathrm{SL_2}(\mathbb{Z})\) the corresponding modular curve has been defined as the quotient space \(\Gamma\backslash\mathcal{H}\), the set of orbits \(\textit{Y}(\Gamma)=\{\Gamma\tau:\tau\in\mathcal{H}\}\)


Riemann Surface Modular Form Elliptic Curve Fundamental Domain Compact Riemann Surface 
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Copyright information

© Springer Science+Business Media New York 2005

Authors and Affiliations

  • Fred Diamond
    • 1
  • Jerry Shurman
    • 2
  1. 1.Department of MathematicsKing’s College London StrandLondonUK
  2. 2.Department of MathematicsReed CollegePortlandUSA

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