| 整函数及其差分分担有限集的唯一性 |
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| 引用本文： | 胡祎,易才凤,徐洪焱.整函数及其差分分担有限集的唯一性[J].数学的实践与认识,2011,41(19). |
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| 作者姓名： | 胡祎 易才凤 徐洪焱 |
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| 作者单位： | 1. 景德镇陶瓷学院信息工程学院,江西景德镇,333403
2. 江西师范大学数信学院,江西南昌,330022 |
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| 基金项目： | 国家自然科学基金(10871108); 江西省自然科学基金(2010GQS0119)); 江西省教育厅青年科学研究项目(GJJ10223); 景德镇陶瓷学院科研资助项目 |
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| 摘 要： | 研究了整函数及其差分多项式分担有限复数集的唯一性,得到了如下结果:设S_m={1,ω,…,ω~(m-1)},其中ω=cos(2π/m)+i sin(2π/m),c为非零有限复数,n(>5),m(≥2)均为正整数.如果f(z),g(z)为有限级整函数,满足E(S_m,f(z)~n(f(z)-1)f(z+c))=E(S_m,g(z)~n(g(z)-1))g(z+c)),那么f(z)≡g(z).
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| 关 键 词： | 整函数 唯一性 分担集 差分 |
On the Uniqueness of Shared Set with Finite Complex Numbers of Differences of Entire Functions |
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| HU Yi,YI Cai-feng,XU Hong-yan.On the Uniqueness of Shared Set with Finite Complex Numbers of Differences of Entire Functions[J].Mathematics in Practice and Theory,2011,41(19). |
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| Authors: | HU Yi YI Cai-feng XU Hong-yan |
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| Institution: | HU Yi~1,YI Cai-feng~2,XU Hong-yan~1 (1.Department of Informatics and Engineering,Jingdezhen Ceramic Institute,Jingdezhen 333403,China) (2.Institute of Mathematics and informatics,Jiangxi Normal University,Nanchang 330022,China |
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| Abstract: | In this paper,we study the uniqueness problems of sharing sets of difference polynomials of entire functions and obtain the following result.Let n(> 5),m(≥2) be two positive integers,c∈C-{0},and S_m={1,ω,…,ω~(m-1)},whereω=cos(2π/m)+ i sin(2π/m).If two nonconstant entire functions f(z),g(z) satisfy E(S_m,,f(z)~n(f(z)-1)f(z+ c))=E(S_m,g(z)~n(g(z)-1))g(z+c)),then f(z)≡g(z). |
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| Keywords: | entire function uniqueness shared set difference |
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