涉及微分多项式分担函数的正规定则

Normality and Shared Function Concerning Differential Polynomials

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].