This book iS the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there iS the unique function satisfying given hypotheses.Developed by R.Nevanlinna，a Finnish mathematician，early in the 1920’S，research in the field has developed rapidly over the past three decades with a great deal of fruitful results.This book systematically summarizes the most important results in the field.including many of the authors’own previously unpublished results.In addition.useful skills and simple proofs are introduced.This book iS suitable for higher level and graduate students who have a basic grounding in complex analysis，but will also appeal to researchers in mathematics.
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目录
Preface Chapter 1 Basic Nevanlinna theory 1.1 The first fundamental theorem 1.2 The second fundamental theorem 1.3 The characteristic function and the order 1.4 The combination of derivatives 1.5 Generalizations of the second fundamental theorem 1.6 Meromorphic functions with two Picard exceptional values 1.7 Combinations ofmeromorphic functions Chapter 2 Unicity of functions of finite(lower)order 2.1 Hadamard's factorization theorem 2.2 Unicitv of meromorphic functions of order＜1 2.3 Functions of finite non-integer(lower)order 2.4 Unicitv of entire functions with finite(lower)order 2.5 Taylor expansions of entire functions with finite order Chapter 3 Five-value，multiple value and uniqueness 3.1 Nevanlinna's five-value theorem 3.2 Lo Yang's method 3.3 Multiple values and uniqueness 3.4 Unicity of meromorphic functions of class Α 3.5 Some general theorems on multiple value and unicity Chapter 4 The four-value theorem 4.1 Nevanlinna'S four-value theorem 4.2 3CM+1IM values theorem 4.3 2CM+2IM values theorem 4.4 DM theorems for entire functions 4.5 4DM theorem Chapter 5 Functions sharing three common values 5.1 Nevanlinna's three-value theorem 5.2 Deficient values and unicity 5.3 Unicity of periodic or even functions 5.4 Unicity of solutions of differential equations 5.5 The relationship between the characteristics 5.6 MÖbius transformation Chapter 6 Three-value sets of meromorphic functions 6.1 Two-value sets of entire functions 6.2 Three-value sets of meromorphic functions Chapter 7 Functions sharing one or two values 7.1 Functions sharing two common values 7.2 Functions sharing one common value Chapter 8 Functions sharing values with their derivatives 8.1 Entire functions 8.2 Meromorphic functions Chapter 9 Two functions whose derivatives share values 9.1 Derivatives sharing common zeros 9.2 Derivatives sharing the value one Chapter 10 Meromorphic functions sharing sets 10.1 Meromorphic functions sharing four sets 10.2 Meromorphic functions sharing three sets 10.3 Meromorphic functions with deficient values 10.4 Meromorphic functions sharing one or two sets 10.5 Preimage and image sets of entire functions 10.6 Unique image sets of meromorphic functions Bibliography Index
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