亚纯函数与其差分分担值的唯一性  

The Uniqueness of Meromorphic Functions and Their Differences Shared Values

作　　者：刘彩燕 聂晓汤 林珊华[2] LIU Caiyan;NIE Xiaotang;LIN Shanhua(College of Mathematics and Statistics,Fujian Normal University,Fuzhou Fujian 350117,China;School of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou Fujian 362000,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]泉州师范学院数学与计算机科学学院,福建泉州362000

出　　处：《泉州师范学院学报》2022年第5期45-50,共6页Journal of Quanzhou Normal University

基　　金：国家自然科学基金资助项目(11801291);福建省自然科学基金(2019J05047,2019J01672,2018R0038)

摘　　要：运用亚纯函数值分布理论,研究亚纯函数具有三个分担值的唯一性问题.结果表明:非常数亚纯函数f(z)与g(z)分担0,∞CM(记重数)且f^(n)(z)与g^(n)(z)分担aCM,则或者f(z)=tg(z),其中t^(n)=1;或者f(z)=be^(α(z)),g(z)=ce^(-α(z)),其中α(z)为整函数,b,c为非零常数且b^(n)c^(n)=a^(2).并将其应用到亚纯函数k阶线性差分算子的唯一性问题中.In this paper,we mainly discussed the uniqueness of meromorphic functions sharing three values by using the knowledge of value distribution theory and the following results were proved:let meromorphic functions f(z)and g(z)sharing 0and∞CM,f^(n)(z)and g^(n)(z)sharing aCM,then either f(z)=tg(z),where t^(n)=1,f(z)=be^(α(z)),g(z)=ce^(-α(z)),whereα(z)be a entire function,b,c be nonzero constant and b^(n)c^(n)=a^(2).It is applied to the uniqueness problem of k-order linear difference operator of meromorphic function.

关 键 词：亚纯函数 差分 分担值 唯一性 

分 类 号：O174.52[理学—数学]