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Preface
Contents
Chapter 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 P′olya 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
Chapter 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 SomeAngular Domains
References
Chapter 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 andIts Derivatives
3.6 Distribution of the Julia, Borel Directions and T Directions
3.7 Singular Directions of Meromorphic Solutions of SomeEquations
3.8 Value Distribution of Algebroid Functions
References
Chapter 4 Argument Distribution and Deficient Values
4.1 Deficient Values and T Directions
4.2 Retrospection
References
Chapter 5 Meromorphic Functions with Radially Distributed Values
5.1 Growth of Such Meromorphic Functions
5.2 Growth of Such Meromorphic Functions with Finite LowerOrder
5.3 Retrospection
References
Chapter 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
Chapter 7 The Potential Theory in Value Distribution
7.1 Signed Measure and Distributions
7.2 δ-Subharmonic Functions
7.2.1 Basic Results Concerningδ-Subharmonic Functions
7.2.2 Normality of Family ofδ-Subharmonic Functions
7.2.3 The Nevanlinna Theory ofδ-Subharmonic Functions
7.3 Eremenko’s Proof of the Nevanlinna Conjecture
References
Index
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