| 亚纯函数的差分多项式 |
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| 引用本文： | 张然然,黄志波. 亚纯函数的差分多项式[J]. 数学年刊A辑(中文版), 2019, 40(2): 127-138 |
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| 作者姓名： | 张然然 黄志波 |
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| 作者单位： | 广东第二师范学院数学系, 广州 510303.,通信作者. 华南师范大学数学科学学院, 广州 510631. |
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| 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)~nH(z,f)-s(z)的零点分布问题.首先得到了差分多项式f(z)~nH(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.
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| 关 键 词： | Difference polynomial Meromorphic function Value distribution |
| 收稿时间： | 2018-01-05 |
| 修稿时间： | 2018-10-07 |
On Certain Type of Difference Polynomials of Meromorphic Functions |
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| ZHANG Ranran and HUANG Zhibo. On Certain Type of Difference Polynomials of Meromorphic Functions[J]. Chinese Annals of Mathematics, 2019, 40(2): 127-138 |
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| Authors: | ZHANG Ranran and HUANG Zhibo |
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| Affiliation: | Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China. and Corresponding author. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China. |
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| Abstract: | 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 thecharacteristic 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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| Keywords: | Difference polynomial Meromorphic function Value distribution |
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