Some Uniqueness Problems Of Meromorphic Functions Concerning Sharing Values

In 1925,the two important basic theories in the system of the value distribution theory of meromorphic functions which was established by the famous Finland mathematician R.Nevanlinna.From then on,the uniqueness theory of meromorphic functions has always been a hot topic in complex analysis.In recent hundred years,many mathematicians had done a lot of work on the research of the value distribution theory of meromorphic functions and got a lot of meaningful results.This thesis mainly discusses the uniqueness of differential polynomials of meromorphic functions with its shift,and studies the uniqueness of meromorphic functions of zero-order with its -shift.The main structure of the thesis is organized as follows:The chapter one is preliminary knowledge.We introduce the Nevanlinna value distribution theory,some fundamental theorems and notations of the uniqueness theory of meromorphic functions,and the difference analogues of value distribution theory of meromorphic functions.In chapter two,we study the uniqueness of differential polynomials of meromorphic functions with its shift of hyper-order less than 1.And we prove an uniqueness theorem for differential polynomials of meromorphic functions satisfies the condition of sharing values partially with its shift,extended the result which was obtained by X.G.Qi,N.Li and L.Z.Yang.In chapter three,we mainly discuss the sharing value problem of meromorphic function with its -shift by using the knowledge of value distribution theory.We show the uniqueness conclusion that under the condition of sharing values partially or values unilaterally with its -shift,improved the result which was obtained by S.J.Chen.In chapter four,we make summary and prospect.We briefly summarize the research content of this thesis,propose the problems to be studied in the next step and put forward some problems that can be further improved.