Some Researches On Uniqueness Of Meromorphic Functions Of Finite Noninteger Order

In 1925,the famous Finnish mathematician R.Nevanlinna founded the value distribution theory of meromorphic functions,which is one of the most important theories of modern function theory.The famous Nevanlinna first and second basic theorems are important contributions to the development of complex analysis.In recent hundred years,the development of the value distribution theory of meromorphic functions is based on the theory of Nevanlinna.In particular,the research on the uniqueness of meromorphic functions has become a popular topic in the field of complex analysis.In the theory of Meromorphic Function Uniqueness,meromorphic functions of finite noninteger order are one of the main objects studied by mathematicians.In this paper,we mainly use Nevanlinna theory of meromorphic function to study meromorphic functions of finite noninteger order with sharing of set or four value.The main structure of the thesis is organized as follows:Chapter 1 is preliminary knowledge.Some basic concepts,common symbols,Nevanlinna value distribution theory and the classical theorem of meromorphic functions uniqueness are briefly introduced.In the second chapter,we study the problem of Gross-Yang and its related properties.First,we study the uniqueness of two common sets shared by a entire function of finite noninteger order and a noninteger entire function.The obtained theorem weakens some conditions in the results obtained by Yi Hongxun.Secondly,we continue to explore the problem of Gross-Yang in the case of meromorphic functions and get the related conclusionsIn the third chapter,we mainly study the uniqueness of sharing four common values between a meromorphic function of finite noninteger order and a noninteger meromorphic function.It improves the results of Sisi Liu and Bin Huang,and gives two concrete examples to illustrate them.Chapter 4 is the summary and prospect.We briefly summarize the research content of this paper,and put forward some problems that can be further studied and improved.