Complex analysis 2
Subtitle: Riemann surfaces, several complex variables, abelian functions, higher modular functions
By: Eberhard Freitag
Series: Universitext; Universitext
Publisher: Springer
Published: 2011
Place of publication: Heidelberg; New York
Language: eng
Number of pages: 506
ISBN-13: 9783642205538; 9783642205545
Subjects: Riemann surfaces; Functions of complex variables; Topology
Description: The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion theorem. This motivates a short introduction into the theory of several complex variables, followed by the theory of Abelian functions up to the theta theorem. The last part of the book provides an introduction into the theory of higher modular functions.
Notes: Includes bibliographical references (p. 494-498) and index.
Table of contents: title: Ch. I. Riemann surfaces; title: Ch. II. Harmonic functions on Riemann surfaces; title: Ch. III. Uniformization; title: Ch. IV. Compact Riemann surfaces; title: Ch. V. Analytic functions of several complex variables; title: Ch. VI. Abelian functions; title: Ch. VII. Modular forms of several variables; title: Ch. VIII. Appendix: algebraic tools.