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
AUTOMORPHIC FUNCTIONS.

Fractional Linear Transformations.

Noneuclidean Geometry.

Discontinuous Groups.

Polygon Groups.

Poincar Series.

The Field of Automorphic Functions.

Automorphic and Algebraic Functions.

Algebraic Curves of Genus 0 and 1, Canonical Polygons.

ABELIAN INTEGRALS.

Reduction, Existence.

The Period Matrix.

The Modular Group.

Canonical Transformation.

The Theorem of Riemann and Roch.

The Theorem of Abel.

The Jacobi Inversion Problem.

Theta Functions.

The Zeros of the Theta Function.

Theta Quotients.

Jacobi-Abel Functions.

Cumulative Index: Vols.

I & II

Topics in Complex Function Theory Volume 2

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    A Paperback / softback by Carl Ludwig Siegel

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      Book details

      Publisher John Wiley & Sons Inc
      Published 30 April 1988
      ISBN-13 9780471608431
      978-0471608431
      ISBN-10 0471608432
      Also in:
      Mathematics

      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
      AUTOMORPHIC FUNCTIONS.

      Fractional Linear Transformations.

      Noneuclidean Geometry.

      Discontinuous Groups.

      Polygon Groups.

      Poincar Series.

      The Field of Automorphic Functions.

      Automorphic and Algebraic Functions.

      Algebraic Curves of Genus 0 and 1, Canonical Polygons.

      ABELIAN INTEGRALS.

      Reduction, Existence.

      The Period Matrix.

      The Modular Group.

      Canonical Transformation.

      The Theorem of Riemann and Roch.

      The Theorem of Abel.

      The Jacobi Inversion Problem.

      Theta Functions.

      The Zeros of the Theta Function.

      Theta Quotients.

      Jacobi-Abel Functions.

      Cumulative Index: Vols.

      I & II

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