[1]方彩云.涉及极点重数的亚纯函数的唯一性[J].东南大学学报(自然科学版),2001,31(5):146-150.[doi:10.3969/j.issn.1001-0505.2001.05.031]
 Fang Caiyun.On Uniqueness of Meromorphic Functions Concerning the Multiplicity of Poles[J].Journal of Southeast University (Natural Science Edition),2001,31(5):146-150.[doi:10.3969/j.issn.1001-0505.2001.05.031]
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涉及极点重数的亚纯函数的唯一性()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
31
期数:
2001年第5期
页码:
146-150
栏目:
数学、物理学、力学
出版日期:
2001-09-20

文章信息/Info

Title:
On Uniqueness of Meromorphic Functions Concerning the Multiplicity of Poles
作者:
方彩云
南京师范大学数学系, 南京 210097
Author(s):
Fang Caiyun
Department of Mathematics, Nanjing Normal University, Nanjing 210097, China)
关键词:
亚纯函数 重数 唯一性
Keywords:
meromorphic function multiplicity uniqueness
分类号:
O174.5
DOI:
10.3969/j.issn.1001-0505.2001.05.031
摘要:
应用值分布理论研究了涉及极点重数的亚纯函数的唯一性问题.得到了下述结论:①设m,n(>9+7/m)是2个正整数, 则存在一个集合S,#S=n, 对于任意一对非常数亚纯函数f(z)与g(z), 如果f(z)与g(z)的极点重数至少是m,且满足条件(-overE)(S,f)=(-overE)(S,g),则f≡g; ② 设k≥3, m, n(>6+4/m)是3个正整数, 则存在一个集合S,#S=n,对于任意一对非常数亚纯函数f(z)与g(z), 如果f(z)与g(z)的极点重数至少是m, 且满足条件Ek(S,f)=Ek(S,g),则f≡g.上述结论推广并改进了 H.X.Yi, M. L. Fang 和H. Guo等人的一些已知结果.
Abstract:
Using the value distribution theory, the author studied the uniqueness of meromorphic functions concerning the multiplicities of their poles. The following results are obtained:① Let m, n(>9+7/m) be two integers. Then there exists a set S with n elements such that (-overE)(S,f)=(-overE)(S,g) can imply f≡g for any pair of nonconstant meromorphic functions f(z) and g(z) and their poles with multiplicity ≥m; ② Let k≥3, m,n(>6+4/m) be three integers. Then there exists a set S with n elements such that Ek(S,f)=Ek(S,g) can imply f≡g for any pair of nonconstant meromorphic functions f(z) and g(z) and their poles with multiplicity ≥m. The above theorems extend and improve some results due to H.X.Yi, M.L.Fang and H.Guo, et al.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介:方彩云,女,1977年生,硕士研究生.
基金项目:国家自然科学基金资助项目(10071038)和江苏省教育厅高等学校自然科学基金资助项目(OOKJB110004).
更新日期/Last Update: 2001-09-20