複分析·2

《複分析·2》是2014年世界圖書出版公司出版的圖書，作者是（德）費萊塔格。

基本介紹

• 中文名：複分析·2 
• 作者：（德）費萊塔格　
• 出版時間：2014年07月
• 出版社：世界圖書出版公司
• ISBN：9787510077838
• 開本：24 開
• 裝幀：平裝

內容簡介

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.

目錄

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