Complex Analysis (Springer-Verlag Berlin and Heidelberg GmbH & Co. KG)

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 kanon 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. TOC:Differential Calculus in the Complex Plane C.- Integral Calculus in the Complex Plane.- 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.- References.- Index.