复与P进位分析中有关值分布及微分性的一些论题

Preface

ListofContributors

PartⅠValueDistributionofComplexandP-adicFunctions

Chapter1TheSecondMainTheoremonGeneralizedParabolicManifolds

1.1Monge-Ampereequationsandgeneralizedparabolicmanifolds

1.2ProjectivizedbundlesoverSteinmanifolds

1.3Meromorphicglobalforms

1.4AnalyticandalgebraicPliickerFormulas:Theclassicalcase

1.5Pluckersformulasforgeneralizedparabolicmanifolds

1.6AnanalogueoftheAhlfors-Stollestimate

1.7Thesecondmaintheorem

Chapter2P-adicValueDistribution

2.1Ultrametricanalyticfunctions

2.2Lazardsproblemandp-adicNevanlinnatheory

2.3ApplicationsoftheNevanlinnatheory

Chapter3SurveyonMeromorphicFunctionsofUniqueness

3.1Introductionandbasicresults

3.2Mainresultsandexamples

Chapter4ASurveyonUniquenessPolynomialsandUniqueRangeSets

4.1Meromorphicfunctionssharingpoints

4.2Uniquerangesetformeromorphicfunctions

4.3Uniquenesspolynomialsformeromorphicfunctions

Chapter5OnPetrenkosTheoryofGrowthofMeromorphicFunctions

5.1Thegrowthoffunctionsmeromorphicintheplane

5.2Thegrowthoffunctionsmeromorphicinthedisc

5.3Separatedmaximummoduluspointsofentireandmeromorphicfunctions

5.4Strongasymptoticvaluesandstrongasymptoticspotsofentireandmeromorphicfunctions

Chapter6LinearOperators,FourierTransformsandtheRiemannξ-function

6.1TheLaguerre-P61yaclassandtheRiemannξ-function

6.2Complexzerodecreasingsequencesandλ-sequences

6.3ThedistributionofzerosofFouriertransforms

6.4InfiniteorderdifferentialoperatorsandtheRiemannξ-function

Chapter7HyperbolicHypersurfacesofLowerDegrees

7.1Introductionandmaintechniques

7.2Hyperboliccurves

7.3Hyperbolicsurfaces

7.4HyperbolichypersurfacesinP4(C)

Chapter8AdmissibleSolutionsofFunctionalEquationsofDiophantineType

8.1Introduction

8.2Backgroundandresults

8.3Preliminarylemmas

8.4Proofsoftheresults

PartⅡNewApplicationsoftheConceptofDifferentiability

Part

　　Therecentadvancements，newresultsandapplicationsofcomplexanalysisandp-adicanalysisareratherextensive．Inthisbook，thefocuscentersonthosetopicswhichpertaintotwointrinsicpropertiesofanalyticfunctions：valuedistributionandcomplexdifferentiability．Complexanalysisandp-adicanalysisaretwocloselylinked，oldbranchesofmathematicsthathaveplayedaprominentroleinthedevelopmentofmodemmathematics．