Topics in complex function theory

著者

• Siegel, Carl Ludwig

書誌事項

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)

収録内容

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

内容説明・目次

巻冊次

v. 3(pbk) ISBN 9780471504016

内容説明

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.

目次

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.

巻冊次

v. 2(pbk) ISBN 9780471608431

内容説明

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.

目次

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

巻冊次

v. 1(pbk) ISBN 9780471608448

内容説明

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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA00099260
• ISBN:
  • 0471790702
  • 0471608440
  • 047179080X
  • 0471608432
  • 0471790907
  • 0471504017
• LCCN: 69019931
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 原本言語コード: ger
• 出版地: New York
• ページ数/冊数: 3 v.
• 大きさ: 23 cm
• 分類:
  • LCC : QA331
  • DC : 515/.9
  • NDC8 : 413.52
• 件名:
  • LCSH : Functions of complex variables
• 親書誌ID:
  • BA00023371