亚纯函数正规族与分担值

Normal Families and Shared Values of Meromorphic Functions

设k,m是两个正整数,a(≠0)是有穷复数.F是区域D内的一族亚纯函数,f∈F的零点重数至少为k,P是多项式,次数或者deg P≥3或者deg P=2且P只有一个不同的零点.若对于F中的任意两个函数f和g,P(f)(f^((k)))~m与P(g)(g^((k)))~m在D内IM分担a,则F在D内正规.

Let k, m be two positive integers, a （≠ 0） be a finite complex number. Let P be a polynomial with either deg P ≥ 3 or deg P = 2, which has only one distinct zero, and F be a family of meromorphic functions in a domain D, all of whose zeros have multiplicities at least k. If, for each pair of functions f and g in F, p（f）（f（k））m and p（g）（g（k））m share an IM in D, then F is normal in D.