A First Course in Modular Forms

• Main Authors: Diamond, Fred (Author), Shurman, Jerry (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2005.
• Series: Graduate Texts in Mathematics, 228
• Subjects: Mathematics.; Algebraic geometry.; Number theory.; Number Theory.; Algebraic Geometry.

This book introduces the theory of modular forms with an eye toward the Modularity Theorem: All rational elliptic curves arise from modular forms. The topics covered include • elliptic curves as complex tori and as algebraic curves, • modular curves as Riemann surfaces and as algebraic curves, • Hec...

Table of Contents:

• Modular Forms, Elliptic Curves, and Modular Curves
• Modular Curves as Riemann Surfaces
• Dimension Formulas
• Eisenstein Series
• Hecke Operators
• Jacobians and Abelian Varieties
• Modular Curves as Algebraic Curves
• The Eichler-Shimura Relation and L-functions
• Galois Representations. .