Modular Forms, Elliptic Curves, and Modular Curves

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


This chapter introduces three central objects of the book.

Modular forms are functions on the complex upper half plane. A matrix group called the modular group acts on the upper half plane, and modular forms are the functions that transform in a nearly invariant way under the action and satisfy a holomorphy condition. Restricting the action to subgroups of the modular group called congruence subgroups gives rise to more modular forms.


Modulus Space Meromorphic Function Modular Form Elliptic Curve Half Plane 
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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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