关于Hayman问题与分担值

设 f 为非常数亚纯函数, n(≥ 4)为正整数, a 为非零有穷复数. 若a 为f ⁿ与 (f ⁿ)′ 的CM分担值, 则nf ’=f.     

SOME NORMALITY CRITERIA OF MEROMORPHIC FUNCTIONS

Let F be a family of functions meromorphic in a domain D, let n ≥ 2 be a positive integer, and let a ≠ 0, b be two finite complex numbers. If, for each f ∈ F, all of whose zeros have multiplicity at least k ＋ 1, and f ＋ a（f^（k））^n≠b in D, then F is normal in D.     

与微分多项式分担值相关的正规定则(英文)

Let F be a family of functions meromorphic in a domain D, let m, n k , k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for eachf∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F,P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and nk ≥ max 1≤i≤k-1 {n i }; (3) m ≥ 2 or nk ≥ 2, k ≥ 2, then F is normal in D.     

涉及微分多项式分担函数的正规定则

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.     

正规族与分担函数（英文）

Let k be a positive integer,let h be a holomorphic function in a domain D,h■0and let F be a family of nonvanishing meromorphic functions in D.If each pair of functions f and q in F,f~((k)) and g~((k)) share h in D,then F is normal in D.