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Lectures on Modular Forms

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Lectures on Modular Forms
Igor V. Dolgachev

Table of Contents

1 Binary Quadratic Forms

2 Complex Tori

3 Theta Functions

4 Theta Constants

5 Transformations of Theta Functions

6 Modular Forms

7 The Algebra of Modular Forms

8 The Modular Curve

9 Absolute Invariant and Cross-Ratio

10 The Modular Equation

11 Hecke Operators

12 Dirichlet Series

13 The Shimura-Tanyama-Weil Conjecture

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