Introduction to arithmetic theory of automorphic functions

Includes index

Includes bibliographical references

Chapter 01: Fuchsian Groups of the First Kind
Chapter 02: Automorphic Forms and Functions
Chapter 03: Hecke Operators and the Zeta-Functions Associated with Modular Forms
Chapter 04: Elliptic Curves
Chapter 05: Abelian Extensions of Imaginary Quadratic Fields and Complex Multiplication of Elliptic Curves
Chapter 06: Modular Functions of Higher Level
Chapter 07: Zeta-Functions of Algebraic Curves and Abelian Varieties
Chapter 08: The Cohomology Group Associated with Cusp Forms
Chapter 09: Arithmetic Fuchsian Groups

The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and, in particular, to elliptic modular forms with emphasis on their number-theoretical aspects.