Modular Functions and Modular Forms

v1.1; May 22, 1997; first version on the web, 128 pages.

Contents

1. Preliminaries
2. Elliptic modular curves as Riemann surfaces
3. Elliptic functions
4. Modular functions and modular forms
5. Hecke operators
6. The modular equation for Gamma_0(N)
7. The canonical model of X_0(N) over Q
8. Modular curves as moduli varieties
9. Modular forms, Dirichlet series, and functional equations
10. Correspondences on curves; the theorem of Eichler and Shimura
11. Curves and their zeta functions
12. Complex multiplication for elliptic curves

Errata