几类亚纯函数q移动微差分多项式的零点与Nevanlinna亏量

The Zeros and Nevanlinna Deficiencies for Some $q$-Shift Difference Differential Polynomials of Meromorphic Functions

中文关键词:  Nevanlinna理论  $q$移动微差分  零级

英文关键词:Nevanlinna theory  $q$-shift difference differential  zero order

中文摘要:

      文章主要讨论了几类亚纯函数的q移动微差分多项式的性质,得到了涉及$q$移动微差分多项式的零点的若干定理. 同时,文章还讨论几类$q$移动微差分单项式的Nevanlinna亏量,得到了关于$\delta(\infty,f)$, $\delta(\infty,f')$, $\delta(\infty,f(z)^nf(qz+c)^mf'(z))$, $\delta(\infty,f(qz+c)^mf'(z))$与$\delta(\infty, f(z)^nf(qz+c)^m)$之间的若干定理.

英文摘要:

      The first purpose of this paper is to study the properties on some $q$-shift difference differential polynomials of meromorphic functions, some theorems about the zeros of some $q$-shift difference-differential polynomials with more general forms are obtained. The second purpose of this paper is to investigate the properties on the Nevanlinna deficiencies for $q$-shift difference differential monomials of meromorphic functions, we obtain some relations among $\delta(\infty,f)$, $\delta(\infty,f')$, $\delta(\infty,f(z)^nf(qz+c)^mf'(z))$, $\delta(\infty,f(qz+c)^mf'(z))$ and $\delta(\infty, f(z)^nf(qz+c)^m)$.