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 D and 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 .
亚纯函数,正规族,Zalcman引理,微分多项式, Meromorphic Function Normal Family Zalcman Lemma Differential Polynomial涉及的零点重级的正规定则
李 菁,赵隽安,邓炳茂. 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[J]. 理论数学, 2016, 06(06): 486-495. http://dx.doi.org/10.12677/PM.2016.66067
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https://doi.org/10.1112/jlms/s1-42.1.389