Modular Functions and Modular Forms

Contents Introduction I The Analytic Theory 1 Preliminaries 2 Elliptic Modular Curves as Riemann Surfaces 3 Elliptic Functions 4 Modular Functions and Modular Forms 5 Hecke Operators II The Algebro-Geometric Theory 6 The Modular Equation for G0(N) 7 The Canonical Model of X0(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-Shimura 11 Curves and their Zeta Functions 12 Complex Multiplication for Elliptic Curves Q Index List of Symbols