This extensive description of classical complex analysis omits sheaf theoretical and cohomological methods to focus on the full quota of essential concepts related to the topic. Lots of exercises and figures make it an ideal introduction to the subject.

The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ¯rst volume. There is no comparable treatment in the literature.

All needed notions are developed within the book with the exception of fundamentals, which are presented in introductory lectures; no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Many exercises including hints for solutions are included

Autorentext
Prof. Dr. Eberhard Freitag, Universität Heidelberg, Mathematisches Institut

Klappentext
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.

Inhalt

Chapter I. Riemann Surfaces.- Chapter II. Harmonic Functions on Riemann Surfaces.- Chapter III. Uniformization.- Chapter IV. Compact Riemann Surfaces.- Appendices to Chapter IV.- Chapter V. Analytic Functions of Several Complex Variables.- Chapter V. Analytic Functions of Several Complex Variable.- Chapter VI. Abelian Functions.- Chapter VII. Modular Forms of Several Variables.- Chapter VIII. Appendix: Algebraic Tools.- References.- Index.