亞純函數值分布理論（簡體書）

《亞純函數值分布理論》共7章，研究在復平面上或在以原點為頂點的角域上亞純的函數的值分布，即通過某些值點來刻畫亞純函數。前兩章研究各類特徵函數及這樣的實函數的性質。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數的增長性的問題在第5章詳細研究。第6章研究亞純函數對應的Riemann曲面，逆函數的奇異性及其與不動點的關係。最后一章介紹具有重要地位的ENevanlinna猜想的Eremenko應用a位勢論的證明。

鄭建華，Dr. Jianhua Zheng is a Professor at the Department of MathematicalSciences, Tsinghua University, China.

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 The Regularity of 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 Nevanlinnas Characteristic in a Domain
2.2 Nevanlinnas Characteristic in an Angle
2.3 Tsujis Characteristic
2.4 Ahlfors-Shimizus 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
4.2 Retrospection
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 Subharmonic Functions
7.2.1 Basic Results Concerning Subharmonic Functions
7.2.2 Normality of Family of Subharmonic Functions
7.2.3 The Nevanlinna Theory of Subharmonic Functions
7.3 Eremenkos Proof of the Nevanlinna Conjecture
References
Index