涉及微分多项式分担函数的正规定则  

Normality and Shared Function Concerning Differential Polynomials

作　　者：邓炳茂[1] 雷春林[1] 方明亮[1] Deng Bingmao;Lei Chunlin;Fang Mingliang(Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642)

机构地区：[1]华南农业大学应用数学研究所,广州510642

出　　处：《数学物理学报（A辑）》2018年第2期222-230,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11371149);华南农业大学博士生国外联合培养(2017LHPY003)~~

摘　　要：设m(≥0)是一个正整数,h(z)(≠0)是区域D内的全纯函数,且其零点重级均≤m,P是多项式满足deg P≥3,或者degP=2且P仅有一个零点.设F是区域D内的一族亚纯函数,其零点与极点重级均≥m+1.如果对于F中的任意两个函数f,g,P(f)f′与P(g)g′分担h(z),则F在区域D内正规.该结果改进了Lei and Fang^([8]),Zhang^([16])等人的结果.Let m（≥ 0） be an integer, let h（z ≠0） be a holomorphic function in a domain D with all zeros have multiplicity at most m, let P be a polynomial with either deg P ≥ 3 or deg P = 2 and P having only one distinct zero, and let 9v be a family of meromorphic functions in a domain D, all of whose zeros and poles have multiplicity at least m ＋ 1. If, for each pair of functions f and g in F, P（f）f＇ and P（g）g＇ share h（z） in D, then F is normal in D. The result improved the results due to Lei and Fang[s], Zhang[16].

关 键 词：亚纯函数 正规定则 分担函数 

分 类 号：O174.5[理学—数学]