一个与分担值相关的亚纯函数正规定则

A Normality of Meromorphic Functions and Shared Values

设D是C内的一个区域,n,k≥2是两个正整数,a是有限非零复数,P是一个多项式,且其次数或者degP≥3,或者degP=2且P只有一个不同零点,F是D内的亚纯函数族,对任意f∈F,f的零点重级至少是k.若F中任意函数f与g,P(f)(f(k))n和P(g)(g(k))n在D内分担a,那么F在D内正规.

Let n,k≥2 be two positive integers,and be a finite non-zero complex number.Let P is a polynomial with either degP≥3 or degP=2 and P having only one distinct zero,and let F be a family of meromorphic functions in a domain D such that each f∈F has only zeros of multiplicty at least k.If for each pair of f and g in F,P（f）（f（k））n and P（g）（g（k））n share the value a,then F is normal in D.