| 微分多项式的例外集 |
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| 引用本文： | 詹小平,文涛.微分多项式的例外集[J].数学学报,1995,38(3):386-394. |
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| 作者姓名： | 詹小平 文涛 |
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| 作者单位： | 湖南师范大学数学系，山东大学数学系 |
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| 基金项目： | 国家自然科学基金，湖南省自然科学基金 |
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| 摘 要： | 设ｆ为任一超越整函数，为ｆ的任一微分多项式；本文证明了在满足｜ａ＿ｎ－ａ＿ｍ｜＞ε｜ａ＿ｎ｜（ｎ≠ｍ）和的无穷个圆盘的并集之外取任意有限非零复数无穷次。
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| 关 键 词： | 整函数 亚纯函数 微分多项式 例外集 |
| 收稿时间： | 1992-2-24 |
| 修稿时间： | 1993-11-18 |
Exceptional Sets for Differential Polynomials |
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| Zhan Xiaoping.Exceptional Sets for Differential Polynomials[J].Acta Mathematica Sinica,1995,38(3):386-394. |
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| Authors: | Zhan Xiaoping |
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| Institution: | Zhan Xiaoping(Department of Mathematics, Hunan Normal University, Changsha 410081,China)Wen Tao(Depatment of Mathematics, Shandong University, Ji’nan 250100, China) |
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| Abstract: | In this paper,we prove the following theorem,Let f be a transcendental entirefunction and be a differential polynomial in f such that.Givenε>0, there exists K=K(ε,γQ,q)>0 such that if(a_n)converges to infinity withfor all n≠n, while(ρ_n)satisfiesthen F-b must have infinitely many zeros outside the union of the discs B(a_n,ρ_n)={z:|z-a_n|<ρ_n)for any b∈C, b≠0.Where γQ is the degree of Q(f). |
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| Keywords: | entire functions meromorphic functionst differential polynomials exceptional sets |
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