| 亚纯函数特征的一个性质 |
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| 引用本文： | 陈翠花 范锡枝. 亚纯函数特征的一个性质[J]. 河南师范大学学报(自然科学版), 1993, 21(4): 22-25 |
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| 作者姓名： | 陈翠花 范锡枝 |
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| 作者单位： | 河南师范大学数学系 453002(陈翠花)，新乡医学院 新乡(范锡枝) |
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| 摘 要： | 本文证明了亚纯函数的一个性质:设b_1、b_2,…是亚纯函数f(z)的极点,|b_1|<|b_2|<…,假设(1)有0<δ_0<1/2,使得对充分大的v,当|b_v|≠|b_(v+1)|时,|b_(v+1)|-|b_v|≥δ_0(|b_0|+1)(2) (3)则对任意小的δ>0,存在R_0(δ)>0,当δR>R_0(δ)时,μ(E_R)≥R~δ其中μ为面积测度E_R={Z;R<|z|<2R,log|f(z)|+N(|z|)>1/2T(R)}
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| 关 键 词： | 亚纯函数的特征 面积测度 |
A Property for Meromorphic Functions''''s Characteristic Number |
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| Chen Cuihua Dept.of Math Henan Normal University,,XinxiangFan Xizhi Medical College of Xinxiang. A Property for Meromorphic Functions''''s Characteristic Number[J]. Journal of Henan Normal University(Natural Science), 1993, 21(4): 22-25 |
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| Authors: | Chen Cuihua Dept.of Math Henan Normal University XinxiangFan Xizhi Medical College of Xinxiang |
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| Affiliation: | Chen Cuihua Dept.of Math Henan Normal University,453002,XinxiangFan Xizhi Medical College of Xinxiang |
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| Abstract: | In this paper,We have proved the following property of meromorphic function:Let b_1,b_2…be all the poles of an meromorphic f(z),|b_1|≤|b_2|≤…,we suppose that.(1)There is a in(0,1/2),such that.|b_(v+1)|-|b_v|≥δ_0(|b_0|+1),(When|b_v|≠|b_(v+1)|)for enough large v.)(2)<+∞,(3)<2Then,there exist some positive number R_0(δ)for any δ>0,such that μ(E_R)≥R~δ when R>R_0(δ)where E_R={z;R<|z|<2R,log|f(z)|+N(|z|)>1/2 T(R)}μis area measure |
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| Keywords: | meromorphic functions characteristic number area measure |
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