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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 |
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