郑秀敏,徐洪焱.几类亚纯函数q移动微差分多项式的零点与Nevanlinna亏量[J].数学研究及应用,2022,42(1):31~40
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
投稿时间:2020-10-19  修订日期:2021-04-07
DOI:10.3770/j.issn:2095-2651.2022.01.004
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
基金项目:国家自然科学基金(Grant Nos.1171035; 11561033), 江西省自然科学基金(Grant No.20181BAB201001), 江西省教育厅科技研究项目(Grant Nos.GJJ190876; GJJ202303; GJJ201813; GJJ191042).
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 
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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 $\delta(\infty, f(z)^nf(qz+c)^m)$.
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