Modular Forms, Elliptic Curves, and Modular Curves
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.
KeywordsModulus Space Meromorphic Function Modular Form Elliptic Curve Half Plane
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