This indispensable book provides an extensive description of classical complex analysis. The authors begin with an introduction to complex analysis that presents the fundamental results, followed by elliptic functions and elliptic modular functions. The book is rounded by excursions to analytic number theory. Great importance is attached to completeness in the sense that all needed notions are developed. More than 400 exercises with hints for solutions are included.

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 Over 400 exercises including hints for solutions are included Includes supplementary material: sn.pub/extras

Autorentext

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

Klappentext

The idea of this book is to give an extensive description of the classical complex analysis, here ''classical'' means roughly that sheaf theoretical and cohomological methods are omitted.

The first four chapters cover the essential core of complex analysis presenting their fundamental results. After this standard material, the authors step forward to elliptic functions and to elliptic modular functions including a taste of all most beautiful results of this field. The book is rounded by applications to analytic number theory including distinguished pearls of this fascinating subject as for instance the Prime Number Theorem. Great importance is attached to completeness, all needed notions are developed, only minimal prerequisites (elementary facts of calculus and algebra) are required.

More than 400 exercises including hints for solutions and many figures make this an attractive, indispensable book for students who would like to have a sound introduction to classical complex analysis.

For the second edition the authors have revised the text carefully.

Inhalt
Differential Calculus in the Complex Plane C.- Integral Calculus in the Complex Plane C.- Sequences and Series of Analytic Functions, the Residue Theorem.- Construction of Analytic Functions.- Elliptic Functions.- Elliptic Modular Forms.- Analytic Number Theory.- Solutions to the Exercises.