Topics in Complex Function Theory, Volume 3: Abelian Functions and Modular Functions of Several Variables (Paperback, Volume 3)

ABELIAN FUNCTIONS.

Power Series in Several Variables.

The Preparation Theorem.

Regular Functions.

Meromorphic Functions.

The Theorem of Weierstrass and Cousin.

The Period Group.

Jacobian Functions.

Linearization of the Exponent System.

The Period Relations.

The Reduced Exponent System.

Existence Proofs.

Picard Varieties.

The Addition Theorem.

MODULAR FUNCTIONS OF SEVERAL VARIABLES.

Automorphic Functions of Several Variables.

Algebraic Relations Between Automorphic Functions.

Symplectic Geometry.

Abelian Functions and Modular Functions.

The Fundamental Region of the Modular Group.

Modular Forms.

The Field of Modular Functions.

Algebraic Dependence.

Bibliography.

Cumulative Index Volumes I, II, and III.