| 关于亚纯函数的0-1-∞集（英） |
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| 引用本文： | 张占亮,朱佃利. 关于亚纯函数的0-1-∞集（英）[J]. 数学研究及应用, 2000, 20(1): 157-158 |
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| 作者姓名： | 张占亮 朱佃利 |
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| 作者单位： | 西江大学;泰安师范学院 |
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| 摘 要： | Let {an}, {bn} and {pn} be three disjoint sequences with no finite limit points. If it is possible to construct a meromorphic function N in the plane whose zeros, one points and poles are exactly {an}, {bn} and {pn} respectively, where their multiplicities are taken into consideration, then the given triple ({an}, {bn}, {Pn}) is called the zero-one-pole set (of N). In general an arbitrary triad ({an}, {bn}, {pn}) is not a zero-one-pole set of any meromorphic function. This was proved by Rubel and Yang[6] explicitly for entire functions. Ozawa[5] proved the following.
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| 文章编号： | 1000-341(2000)01-0157-02 |
| 收稿时间： | 1996-08-27 |
| 修稿时间： | 1996-08-27 |
On the Zero-One-Pole Set of a Meromorphic Function |
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| ZHANG Zhao-liang and ZHU Dian-li. On the Zero-One-Pole Set of a Meromorphic Function[J]. Journal of Mathematical Research with Applications, 2000, 20(1): 157-158 |
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| Authors: | ZHANG Zhao-liang and ZHU Dian-li |
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| Affiliation: | 1. Dept. of Math., Xijiang University, Zhaoqing 256061, Guangdong
2. Dept. of Math., Taian Teaching College. Taian 271000 |
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| Abstract: | Let {an}, {bn} and {pn} be three disjoint sequences with no finite limit points. If it is possible to construct a meromorphic function N in the plane whose zeros, one points and poles are exactly {an}, {bn} and {pn} respectively, where their multiplicities are taken into consideration, then the given triple ({an}, {bn}, {Pn}) is called the zero-one-pole set (of N). In general an arbitrary triad ({an}, {bn}, {pn}) is not a zero-one-pole set of any meromorphic function. This was proved by Rubel and Yang[6] explicitly for entire functions. Ozawa[5] proved the following. |
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| Keywords: | unicity meromorphic funiction. |
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