亚纯函数多项式与其导函数分担小函数的唯一性  

Uniqueness on the polynomials of meromorphic functions sharing a small function with their derivatives

作　　者：刘登峰 吴爱迪 Liu Dengfeng;Wu Aidi(College of Mathematics and Statistics,Fujian Normal University,Fuzhou 3501i,China;College of Computer and Information Sciences,Fujian Agriculture and Forestry University,Fuzhou 350002,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]福建农林大学计算机与信息学院,福建福州350002

出　　处：《纯粹数学与应用数学》2022年第4期473-481,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11801291);福建省自然科学基金(2019J05047,2019J01672,2020R0039)。

摘　　要：利用Nevanlinna理论与多项式加权和的概念研究了一类亚纯函数多项式与其导函数分担小函数的唯一性.在分担小函数的条件下,得到了亚纯函数的特征函数与计数函数之间的一个不等式,并研究了亚纯函数多项式与其k阶导数分担小函数的唯一性问题,所得到的定理补充,改进与推广了一些已有的结果.Using Nevanlinna Theory and the concept of weighted sum of polynomials,the authors study the uniqueness problems of polynomials of meromorphic functions with their derivatives sharing a small function.Under the premise of sharing small function,the authors obtain one inequality for the relationship of the characteristic function and pole counting function of f(z),and study the uniqueness problems of polynomials of meromorphic functions sharing a small function with their k-th derivatives,which supplement,improve and extend some known results.

关 键 词：亚纯函数 导函数 小函数 唯一性 

分 类 号：O178[理学—数学]