限制零点个数的亚纯函数的正规定则

Some Normal Criteria of Meromorphic Functions Limited the Numbers of Zeros

设k,n(≥k+1)是两个正整数,a(≠0),b是两个有穷复数,F为区域D内的一族亚纯函数.如果对于任意的f∈F,f的零点重级大于等于k+1,并且在D内满足f+a[L(f)]~n-b至多有n-k-1个判别的零点,那么F在D内正规·这里L(f)=f^((k))(z)+a_1f^((k-1))(z)+…+a_(k-1)f'(z)+a_kf(z),其中a_1(z),a_2(z),…,a_k(z)是区域D上的全纯函数.

Let k,n(≥ k+1) be two positive integers, a(≠0), b be two finite complex numbers and F be a family of meromorphic functions in D. If for each function f∈ F, all zeros of f have multiplicity at least k +1, and f + a(L(f))n-b has at most n-k-1 distinct zeros in D, then F is normal in D, where L(f)= f(k)(z)+ a1 f^(k-1)(z)+…+ ak-1f’(z)+akf(z),a1(z), a2(z),…, ak(z) are holomorphic functions in D.