Topics in complex function theory

Author(s)

• Siegel, Carl Ludwig

Bibliographic Information

Topics in complex function theory

by C. L. Siegel ; translated from the original German by A. Shenitzer ... [et al.]

（Interscience tracts in pure and applied mathematics, 25）

Wiley-Interscience, c1969-01973

• v. 1
• v. 1(pbk)
• v. 2
• v. 2(pbk)
• v. 3
• v. 3(pbk)

Contents of Works

• v. 1. Elliptic functions and uniformization theory
• v. 2. Automorphic functions and Abelian integrals
• v. 3. Abelian functions and modular functions of several variables

Description and Table of Contents

Volume

v. 3(pbk) ISBN 9780471504016

Description

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.

Volume

v. 2(pbk) ISBN 9780471608431

Description

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

Volume

v. 1(pbk) ISBN 9780471608448

Description

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.

by "Nielsen BookData"

Details

• NCID: BA00099260
• ISBN:
  • 0471790702
  • 0471608440
  • 047179080X
  • 0471608432
  • 0471790907
  • 0471504017
• LCCN: 69019931
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: ger
• Place of Publication: New York
• Pages/Volumes: 3 v.
• Size: 23 cm
• Classification:
  • LCC : QA331
  • DC : 515/.9
  • NDC8 : 413.52
• Subject Headings:
  • LCSH : Functions of complex variables
• Parent Bibliography ID:
  • BA00023371