Value distribution theory Book

Ch. 1	Essentials of Nevanlinna Theory	1
1.1	The Poisson-Jensen Formula	1
1.2	Characteristic Functions and the First Fundamental Theorem	5
1.3	The Second Fundamental Theorem	13
1.4	Applications of the Second Fundamental Theorem	25
1.5	Generalizations of the Second Fundamental Theorem	34
Ch. 2	Normal Families	42
2.1	Normal Families of Holomorphic Functions	42
2.2	Montel's Criterion	47
2.3	Montel Cycle, Normal Families of Meromorphic Functions	54
Ch. 3	Borel Directions	58
3.1	Preliminaries	58
3.2	Fundamental Theorems	65
3.3	Filling Disks and Borel Directions	75
3.4	Properties of Borel Directions	85
Ch. 4	Value Distribution of Meromorphic Functions Together with Their Derivatives	93
4.1	Comparison Between Growths of Tr, f and Tr, f'	93
4.2	Modular Distribution of Meromorphic Functions Together with Their Derivatives	99
4.3	An Inequality of Hayman	108
4.4	A General Criterion for Normality	112
4.5	Total Deficiency of Meromorphic Derivatives	121
4.6	A New Method for Proving Normality	131
Ch. 5	Recent Studies on Borel Directions	138
5.1	Distribution of Borel Directions	138
5.2	Common Borel Directions of a Meromorphic Function and Its Derivatives	148
5.3	Angular Distribution of Meromorphic Functions Together with Their Derivatives	163
Ch. 6	Deficient Values and Borel Directions of Meromorphic Functions	172
6.1	Precise Order and Three Lemmas	172
6.2	Distribution of Borel Directions of Meromorphic Functions with Deficient Values	184
6.3	Deficient Values and Borel Directions of Meromorphic Functions	190
6.4	Deficient Values, Borel Directions and the Order of Entire Functions	197
Ch. 7	The Spread Relation and Its Applications	216
7.1	Sequence of Polya Peaks and Its Existence	216
7.2	The T* Function	221
7.3	The Spread Relation	231
7.4	Applications of the Spread Relation	240
7.5	The Deficiency Problem	246
	Bibliography	259
	Index	269