高阶q-差分多项式的值分布

The Value Distribution of q-difference Polynomials of High Order

研究了高阶q-差分多项式的值分布性质．特别地，利用Nevanlinna理论考虑了差分多项式f（z）^n△q^kf（z）-a（z）及其导数的零点分布，其中q∈C＼{0，1}是使得△q^kf（z）≠0的常数，a（z）（≠0，∞）是f（z）的小函数．

In this paper, we investigate the value distribution of q-difference polynomials of high order. In particular, by using Nevanlinna theory, we consider the zero distribution of q-difference polynomials f（z）^n△q^kf（z）-a（z） and its derivative, where q∈C／{0,1} is a constant such that △q^kf（z）≠0, and a（z）（≠0, ∞） is a small function with respect to f（z）.