On The Value Distribution And Uniqueness Of The Q-difference Polynomials Of Meromorphic Function

In this paper,we mainly study the value distributions and uniqueness theorems of q dif-ference polynomials of entire function and meromorphic function,the value distributions and uniqueness theorems of q difference polynomials of Hayman conjecture,and the zero distribu-tions of a kind of finite logarithm orderλ_log（f）transcendental meromorphic function.They are some interesting researches in the complex analysis.The thesis is orgnized as follows.The first chapter,we introduce the background and present situation of the research on complex domain difference equation,q difference equation,and the corresponding uniqueness theory of difference simulation.The second chapter,some basic knowledge of Nevanlinna theory and its difference ana-logues are briefly introduced.In Chapter three,we use linear q-difference polynomials to study the classical results of Hayman’s conjecture.The results of Chen Meiru and Chen Zongxuan and Zhang J.L.and Korhone R are generalized.In Chapter four,we study the difference result of q and the uniqueness theorem of Hay-man conjecture.The results of Liu Kai and Qi Xiaoguang,Zhang Xiaobin and Yi Hongxun are generalized.In Chapter five,we study the value distribution and uniqueness of the q-type difference polynomials of Meromorphic functions of zero order.The results of Zhang Xiaobin and Yi Hongxun,Cao Tingbin,Liu Kai,and Xu Na are generalized.In Chapter six,we study the distribution of zeros of a class of transcendental meromorphic functions of finite logarithmic orderλ_log（f）.The results of Xu Jufeng and Zhang Xiaobin,Cao Tingbin,Liu Kai and Xu are popularized.