亚纯函数与其微分多项式的分担值与正规族

Normality and shared values concerning meromorphic functions differential polynomials

设F为区域D上的一族亚纯函数,所有的零点重级至少是k,b为有穷非零复数,n,k为两正整数,P是有三个互相判别的零点的多项式.如果任意函数f,g∈F,P(f)(fn)(k)和P(g)(gn)(k)在D内分担b,则F在D内正规.

Let F be a family of meromorphic functions in a domain D , all of whose zeros having multi-plicities at least k , let b be a finite nonzero complex number, n , k be two positive integers, and let P be a polynomial with three distinct zeros. If each pair of functionsf and g in F , P（f）（f^n）^（k）, and p（g） （ g^n ）^（k） share b in D , then F is normal on D.