Uniqueness Of Displacement And Difference Of Meromorphic Functions

The uniqueness of meromorphic functions is one of the impor-tant and active research topic of Nevanlinna theory. In recent years, the uniqueness research has extended to difference field. This article mainly discusses some research on the uniqueness of shift, q-shift and difference of meromorphic function on sharing constant (or small functions) problem. Some meaningful results are obtained. The structure of the thesis is as followed.In preface, we simply summarize the development background and some research achievements of the value distribution theory and uniqueness theory of meromorphic functions.In the first chapter, we will give some basic knowledge of value dis-tribution theory and uniqueness theory, such as some basic concepts, notations and basic results.In the second chapter, we mainly study the problem of the unique-ness of meromorphic functions involving shift and difference shared the small function, and we obtained the corresponding results of Yi Hongxun and Yang Chongjun [19] about derivative uniqueness, which improve the results about difference uniqueness due to Liu Yong and Qi Xiaoguang [20].In the third chapter, We mainly study the problem of the unique-ness of meromorphic function involving q-shift, which promote the results due to Qi Xiaoguang and Yang Lianzhong [22], Zhang and Korhonen [24], Wang Qiongyan and Ye Yasheng [25].