亚纯函数值分布理论

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

《亚纯函数值分布理论》共7章，研究在复平面上或在以原点为顶点的角域上亚纯的函数的值分布，即通过某些值点来刻画亚纯函数。前两章研究各类特征函数及这样的实函数的性质。第3、4章放在新引入的奇异方向——T方向，包括存在性、分布，与其他方向的关系上，T方向与分布值和亏值总数的关系。射线分布值确定亚纯函数的增长性的问题在第5章详细研究。第6章研究亚纯函数对应的Riemann曲面，逆函数的奇异性及其与不动点的关系。最后一章介绍具有重要地位的ENevanlinna猜想的Eremenko应用a位势论的证明。

Value Distribution of Meromorphic Functions focuses on functionsmeromorphic in an angle or on the complex plane， T directions， deficientvalues， singular values， potentia·theory in value distribution and theproof of the celebrated Nevanlinna conjecture. The book introducesvarious characteristics of meromorphic functions and their connections，severa·aspects of new singular directions， new results on estimates of thenumber of deficient values， new results on singular values and behavioursof subharmonic functions which are the foundation for further discussionon the proof of the Nevanlinna conjecture. The independent significanceof normality of subharmonic function family is emphasized. This book isdesigned for scientists， engineers and post graduated students engaged inComplex Analysis and Meromorphic Functions.