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

DOI：10.3770/j.issn:2095-2651.2022.01.004

 作者 单位 郑秀敏 江西师范大学数学与统计学院, 江西 南昌 334001 徐洪焱 江西师范大学数学与统计学院, 江西 南昌 334001 上饶师范学院数学与计算机科学学院, 江西 上饶 330022

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.

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 $\delta(\infty, f(z)^nf(qz+c)^m)$.