Study On The Second Fundamental Theorem And The Uniqueness Of Algebroid Functions

The last century, Finland mathematician Nevanlinna introduced the characteristicfunction. Based on it, he establish two basic theorems of meromorphic functions, thuscreated the value distribution theory of modern research. Over half a century, a largenumber of domestic and international mathematicians in this field performed a lot ofresearch based on the theory of value distribution of meromorphic functions and algebraFunctions. In this paper, using the meromorphic functions and algebroid function valueanalysis theory, we investigate the related properties and expansion of the secondfundamental theorem of algebroid function, and discusse the uniqueness of algebroidfunctions.This thesis is divided into five parts:In chapter one, we introduce the basic knowledge of distribution theory and basictheorems of meromorphic functions and algebroid function value, expounds the theoreticalachievements and the development of the uniqueness theory.In chapter two, by using the value distribution theory of algebroid function, weinvestigate the second fundamental theorem of algebroid function relates to polynomial,improved the conclusions of Xiong Qinglai, Wu Xiao and so on.In chapter three, using the second fundamental theorem of algebroid function relatesto polynomial and derivative of the function of, we get some promotion forms of thesecond basic theorem.In chapter four, through the second basic theorems involving polynomials, we discussthe uniqueness of the function, and extend the related results in the literature...