标题:
涉及fnf(k)+H(f)-b 的零点重级的正规定则A Normality Criterion Concerning the Zeros’ Multiplicity of fnf(k)+H(f)-b
作者:
李菁, 赵隽安, 邓炳茂
关键字:
亚纯函数, 正规族, Zalcman引理, 微分多项式Meromorphic Function, Normal Family, Zalcman Lemma, Differential Polynomial
期刊名称:
《Pure Mathematics》, Vol.6 No.6, 2016-11-28
摘要:
本文研究全纯函数族的正规性,证明了如下结论：设M，n，k为三个正整数，其中当n=k=1 时，M≥9 ；当nk>1 时， ，b 为一个非零有穷复数，设F 为区域D 内的一族全纯函数，H(f) 为f 的微分多项式且满足 ，若对于F 中的每一个函数f(z) 均有(1)f(z) 的零点重级≥k ；(2)f(n)f(k)+H(f)-b的零点重级≥M ，则F 在D 内正规。
In this paper, we study the normality of holomorphic functions and prove the following results: Let M, n, k be three positive integers satisfying M≥9 when n=k=1 and when nk>1, b(≠0) , is a finite complex number; let F be a family of holomorphic functions in a domain Dand H(f) be a differential polynomial of f and satisfy , if for each f∈ F , satisfies (1) all zeros of f have multiplicity at least k; (2) all zeros of f(n)f(k)+H(f)-b have multiplicity ≥M , then F is normal in D .