Some Researches On The Uniqueness Of Meromorphic Functions

In 1925,R.Nevanlinna founded the value distribution theory of meromorphic functions,which is one of the most important theories of modern function theory.With the development of Nevanlinna theory,many research fields of complex analysis have been developing rapidly.Especially,the value distribution theory of meromorphic functions concerning their shifts and difference operators has achieved many excellent results in the past two decades,and lots of scholars are interested in the topic.In this thesis,we study the uniqueness of meromorphic functions concerning their shifts,and that of differential-difference polynomials.The dissertation is structured as follows.In chapter one is preliminary knowledge.We mainly describe the relevant research results of Nevanlinna theory,uniqueness theory of meromorphic functions,difference simulation theory and so on.In chapter two,we mainly study the uniqueness of 6)-order derivatives of meromorphic function and its shift partial shared value.Moreover,our results generalize and improve the results of Qi Xiaoguang et al.In chapter three,using the idea of weight sharing,we study the uniqueness of differential-difference polynomials of meromorphic functions concerning sharing value,which improves the results obtained by Liu Kai,Li Xiaomin and Yi Hongxun.In chapter four,we investigate the uniqueness of meromorphic functions with hyper-order less than 1 and their shifts sharing two sets.Our theorems weaken the condition of the shared set from CM sharing to partial sharing.Chapter five 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.