| 张然然,黄志波.亚纯函数的差分多项式[J].数学年刊A辑,2019,40(2):127~138 |
| 亚纯函数的差分多项式 |
| On Certain Type of Difference Polynomials of Meromorphic Functions |
| Received:January 05, 2018 Revised:October 07, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0011 |
| 中文关键词: Difference polynomial, Meromorphic function,Value distribution |
| 英文关键词:Difference polynomial, Meromorphic function,Value distribution |
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| 中文摘要: |
| 假设函数 $f(z)$ 是亚纯函数, $H(z,f)$ 是关于 $f(z)$ 的差分多项式, $s(z)$ 是关于
$f(z)$ 的小函数, 考察了差分多项式 $f(z)^{n} H(z,f)-s(z)$ 的零点分布问题.
首先得到了差分多项式 $f(z)^{n} H(z,f)-s(z)$ 的零点计数函数和函数 $f(z)$
的特征函数以及极点计数函数之间的一些不等式估计, 再根据这些不等式,
建立了Hayman关于亚纯函数的一个经典结果的差分模拟. |
| 英文摘要: |
| In this paper, the authors investigate zeros of difference polynomials of the form
$f(z)^{n} H(z, f)-s(z)$, where $f(z)$ is a meromorphic function, $H(z, f)$ is a difference polynomial of $f(z)$ and $s(z)$ is a small function.
The authors first obtain some inequalities for the relationship of the zero counting function of $f(z)^nH(z, f)-s(z)$ and the
characteristic function and pole counting function of $f(z)$.
Based on the above inequalities, the authors then establish some difference analogues of a classical result of Hayman for meromorphic functions. |
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