【内容简介】: This book is a translation of the forthcoming fourth edition of our German book "Funktionentheorie P' (Springer 2005). The translation and the LATEX files have been produced by Dan Fulea. He also made a lot of suggestions for improvement which influenced the English version of the book. It is a pleasure for us to express to him our thanks. We also want to thank our colleagues Diarmuid Crowley, Winfried Kohnen and Jorg Sixt for useful suggestions concerning the translation.
【目录】:
Differential Calculus in the Complex Plane C Ⅰ.1 Complex Numbers Ⅰ.2 Convergent Sequences and Series Ⅰ.3 Continuity Ⅰ.4 Complex Derivatives Ⅰ.5 The CAUCHY-RIEMANN Differential Equations Ⅱ Integral Calculus in the Complex Plane C Ⅱ.1 Complex Line Integrals Ⅱ.2 The CAUCHY Integral Theorem Ⅱ.3 The CAUCHY Integral Formulas Ⅲ Sequences and Series of Analytic Functions, the Residue Theorem Ⅲ.1 Uniform Approximation Ⅲ.2 Power Series Ⅲ.3 Mapping Properties of Analytic Functions Ⅲ.4 Singularities of Analytic Functions Ⅲ.5 LAURENT Decomposition A Appendix to III.4 and III.5 Ⅲ.6 The Residue Theorem Ⅲ.7 Applications of the R,esidue Theorem Ⅳ Construction of Analytic Functions Ⅳ.1 The Gamma Function Ⅳ.2 The WEIERs'rRASS Product Formula Ⅳ.3 The MITrrAc_LEFFLER Partial FYaction Decomposition Ⅳ.4 The RIEMANN Mapping Theorem A Appendix : The Homotopical Version of the CAUCHY Integral Theorem B Appendix : A Homological Version of the CAUCHY Integral Theorem C Appendix : Characterizations of Elementary Domains Ⅴ Elliptic Functions Ⅴ.1 LIOUViLLE'S Theorems A Appendix to the Definition of the Period Lattice Ⅴ.2 The WEIERSTRASS -function Ⅴ.3 The Field of Elliptic Functions A Appendix to Sect. V.3 : The Torus as an Algebraic Curve Ⅴ.4 The Addition Theorem Ⅴ.5 Elliptic Integrals Ⅴ.6 ABEL'S Theorem Ⅴ.7 The Elliptic Modular Group Ⅴ.8 The Modular Function j Ⅵ Elliptic Modular Forms Ⅵ.1 The Modular Group and Its Fundamental Region Ⅵ.2 The k/12-formula and the Injectivity of the j-function Ⅵ.3 The Algebra of Modular Forms Ⅵ.4 Modular Forms and Theta Series Ⅵ.5 Modular Forms for Congruence Groups A Appendix to V1.5 : The Theta Group Ⅵ.6 A Ring of Theta Fhnctions Ⅶ Analytic Number Theory Ⅶ.1 Sums of Four and Eight Squares Ⅶ.2 DIRiCHLErr Series Ⅶ.3 DIRICHLET Series with Functional Equations Ⅶ.4 The RIEMANN <-function and Prime Numbers Ⅶ.5 The Analytic Continuation of the <-function Ⅶ.6 A TAUBERian Theorem Ⅷ Solutions to the Exercises Ⅷ.1 Solutions to the Exercises of Chapter Ⅰ Ⅷ.2 Solutions to the Exercises of Chapter Ⅱ Ⅷ.3 Solutions to the Exercises of Chapter Ⅲ Ⅷ.4 Solutions to the Exercises of Chapter Ⅳ Ⅷ.5 Solutions to the Exercises of Chapter Ⅴ Ⅷ.6 Solutions to the Exercises of Chapter Ⅵ Ⅷ.7 Solutions to the Exercises of Chapter Ⅶ R/eferences Symbolic Notations
以下为对购买帮助不大的评价