| 《亚纯函数值分布理论》：Value Distribution of Meromorphic Functions focuses on functionsmeromorphic in an angle or on the complex plane, T directions, deficientvalues, singular values, potential theory in value distribution and theproof of the celebrated Nevanlinna conjecture. The book introducesvarious characteristics of meromorphic functions and their connections,several 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. |
| 郑建华，Dr. Jianhua Zheng is a Professor at the Department of MathematicalSciences, Tsinghua University, China. |
| 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 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 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 8-subharmonic functions 7.2.1 basic results concerning 8-subharmonic functions 7.2.2 normality of family of 8-subharmonic functions 7.2.3 the nevanlinna theory of 8-subharmonic functions 7.3 eremenko's proof of the nevanlinna conjecture references index |
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