內容簡介
本書共7章，研究在複平面上或在以原點為頂點的角域上亞純的函式的值分布，即通過某些值點來刻畫亞純函式。前兩章研究各類特徵函式及這樣的實函式的性質。第3、4章放在新引入的奇異方向——T方向，包括存在性、分布，與其他方向的關係上，T方向與分布值和虧值總數的關係。射線分布值確定亞純函式的增長性的問題在第5章詳細研究。第6章研究亞純函式對應的Riemann曲面，逆函式的奇異性及其與不動點的關係。最後一章介紹具有重要地位的ENevanlinna猜想的Eremenko套用位勢論的證明。
目錄
1 Preliminaries of Real Functions
1.1 Functions of a Real Variable
1.1.1 The Order and Lower Order of a Real Function
1.1.2 The P61ya Peak Sequence of a Real Function
1.1.3 Theregularityof a Real Function
1.1.4 Quasi-invariance of Inequalities
1.2 Integral Formula and Integral Inequalities
1.2.1 The Green Formula for Functions with Two Real Variables
1.2.2 Several Integral Inequalities
References
2 Characteristics of a Meromorphic Function
2.1 Nevanlinna's Characteristic in a Domain
2.2 Nevanlinna's Characteristic in an Angle
2.3 Tsuji's Characteristic
2.4 Ahlfors-Shimizu's Characteristic
2.5 Estimates of the Error Terms
2.6 Characteristic of Derivative of a Meromorphic Function
2.7 Meromorphic Functions in an Angular Domain
2.8 Deficiency and Deficient Values
2.9 Uniqueness of Meromorphic Functions Related to Some Angular Domains
References
3 T Directions of a Meromorphic Function
3.1 Notation and Existence of T Directions
3.2 T Directions Dealing with Small Functions
3.3 Connection Among T Directions and Other Directions
3.4 Singular Directions Dealing with Derivatives
3.5 The Common T Directions of a Meromorphic Function and Its Derivatives
3.6 Distribution of the Julia, Borel Directions and T Directions
3.7 Singular Directions of Meromorphic Solutions of Some Equations
3.8 Value Distribution of Algebroid Functions
References
4 Argument Distribution and Deficient Values
4.1 Deficient Values and T Directions
References
5 Meromorphic Functions with Radially Distributed Values
5.1 Growth of Such Meromorphic Functions
5.2 Growth of Such Meromorphic Functions with Finite Lower Order
5.3 Retrospection
References
6 Singular Values of Meromorphic Functions
6.1 Riemann Surfaces and Singularities
6.2 Density of Singularities
6.3 Meromorphic Functions of Bounded Type
References
7 The Potential Theory in Value Distribution
7.1 Signed Measure and Distributions
7.2 8-Subharmonic Functions
7.2.1 Basic Results Concerning 8-Subharmonic Functions
7.2.2 Normality of Family of 8-Subharmonic Functions
7.2.3 The Nevanlinna Theory of 8-Subharmonic Functions
7.3 Eremenko's Proof of the Nevanlinna Conjecture
References
Index
