复分析（第2版）

图书标准信息

• 作者 [德]弗莱塔格 著
• 出版社 世界图书出版公司
• 出版时间 2014-07
• 版次 2
• ISBN 9787510077838
• 定价 89.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 532页
• 正文语种 英语

【内容简介】

　　ThisbookisatranslationoftheforthcomingfourtheditionofourGermanbook"FunktionentheorieP'(Springer2005).ThetranslationandtheLATEXfileshavebeenproducedbyDanFulea.HealsomadealotofsuggestionsforimprovementwhichinfluencedtheEnglishversionofthebook.Itisapleasureforustoexpresstohimourthanks.WealsowanttothankourcolleaguesDiarmuidCrowley,WinfriedKohnenandJorgSixtforusefulsuggestionsconcerningthetranslation.

【目录】

DifferentialCalculusintheComplexPlaneC
Ⅰ.1ComplexNumbers
Ⅰ.2ConvergentSequencesandSeries
Ⅰ.3Continuity
Ⅰ.4ComplexDerivatives
Ⅰ.5TheCAUCHY-RIEMANNDifferentialEquations

ⅡIntegralCalculusintheComplexPlaneC
Ⅱ.1ComplexLineIntegrals
Ⅱ.2TheCAUCHYIntegralTheorem
Ⅱ.3TheCAUCHYIntegralFormulas

Ⅲ　SequencesandSeriesofAnalyticFunctions,theResidue　Theorem
Ⅲ.1UniformApproximation
Ⅲ.2PowerSeries
Ⅲ.3MappingPropertiesofAnalyticFunctions
Ⅲ.4SingularitiesofAnalyticFunctions
Ⅲ.5LAURENTDecomposition　AAppendixtoIII.4andIII.5
Ⅲ.6TheResidueTheorem
Ⅲ.7ApplicationsoftheR,esidueTheorem

ⅣConstructionofAnalyticFunctions
Ⅳ.1TheGammaFunction
Ⅳ.2TheWEIERs'rRASSProductFormula
Ⅳ.3TheMITrrAc_LEFFLERPartialFYactionDecomposition
Ⅳ.4TheRIEMANNMappingTheorem
AAppendix:TheHomotopicalVersionoftheCAUCHY　IntegralTheorem
BAppendix:AHomologicalVersionoftheCAUCHY
IntegralTheorem
CAppendix:CharacterizationsofElementaryDomains

ⅤEllipticFunctions
Ⅴ.1LIOUViLLE'STheorems
AAppendixtotheDefinitionofthePeriodLattice
Ⅴ.2TheWEIERSTRASS-function
Ⅴ.3TheFieldofEllipticFunctions
AAppendixtoSect.V.3:TheTorusasanAlgebraicCurve
Ⅴ.4TheAdditionTheorem
Ⅴ.5EllipticIntegrals
Ⅴ.6ABEL'STheorem
Ⅴ.7TheEllipticModularGroup
Ⅴ.8TheModularFunctionj

ⅥEllipticModularForms
Ⅵ.1TheModularGroupandItsFundamentalRegion
Ⅵ.2Thek/12-formulaandtheInjectivity　ofthej-function
Ⅵ.3TheAlgebraofModularForms
Ⅵ.4ModularFormsandThetaSeries
Ⅵ.5ModularFormsforCongruenceGroups
AAppendixtoV1.5:TheThetaGroup
Ⅵ.6ARingofThetaFhnctions

Ⅶ　AnalyticNumberTheory
Ⅶ.1SumsofFourandEightSquares
Ⅶ.2DIRiCHLErrSeries
Ⅶ.3DIRICHLETSerieswithFunctionalEquations
Ⅶ.4TheRIEMANN<-functionandPrimeNumbers
Ⅶ.5TheAnalyticContinuationofthe<-function
Ⅶ.6ATAUBERianTheorem

ⅧSolutionstotheExercises
Ⅷ.1SolutionstotheExercisesofChapterⅠ
Ⅷ.2SolutionstotheExercisesofChapterⅡ
Ⅷ.3SolutionstotheExercisesofChapterⅢ
Ⅷ.4SolutionstotheExercisesofChapterⅣ
Ⅷ.5SolutionstotheExercisesofChapterⅤ
Ⅷ.6SolutionstotheExercisesofChapterⅥ
Ⅷ.7SolutionstotheExercisesofChapterⅦ
R/eferences
SymbolicNotations