The Study Of The Value Distribution Of Difference Polynomials And Difference-Differential Polynomials

Recently,wifh the development of difference analogue of Nevanlinna theory, many authors paid their attentions to the value distribution of difference polynomials and difference equations. In this paper, the value distribution of q-difference polynomials and difference-differential polynomials has been considered.This paper is arranged as follows:In Chapter1,the background of the research is given,and the major work of this paper is introduced.In Chapter2,we give some theorems of difference analogue of Nevanlinna fheory,and bring in some related definitions and signs.In Chapter3,we investigate the value distribution of q-difference polynomials of meromorphic functions of finite logarithmic order,and study the zero distribution of difference-differential polynomials[fn(z)f()qz+c)](k) and [fn(z)(f(qz+c)-f(z))](k) where f(z) is a transcendental function of zero order.The uniqueness problem of difference-differenfial polynomial[fn(z)(fm(z)-a)f(qz+c)](k) is also considered.In Chapter4,we discuss the value distribution of q-difference differential polynomials[f(z)(f(qZ)-f(Z))](k) and [f(z)f(qz)](k),where f(z)is a transcendental entire function with order,0<σ(f)<∞...