Description

Book Synopsis
Develops the higher parts of function theory in a unified presentation. Starts with elliptic integrals and functions and uniformization theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular functions in several variables. The last topic originates with the author and appears here for the first time in book form.

Table of Contents
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.

Topics in Complex Function Theory Volume 3

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    A Paperback / softback by Carl Ludwig Siegel

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      Book details

      Publisher John Wiley & Sons Inc
      Published 19 April 1989
      ISBN-13 9780471504016
      978-0471504016
      ISBN-10 0471504017
      Also in:
      Mathematics Functional analysis and transforms

      Description

      Book Synopsis
      Develops the higher parts of function theory in a unified presentation. Starts with elliptic integrals and functions and uniformization theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular functions in several variables. The last topic originates with the author and appears here for the first time in book form.

      Table of Contents
      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.

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