涉及高阶导数的分担函数与正规族
Sharing functions and normal families involving higher-order derivatives
王皓然 1杨祺1
作者信息
- 1. 新疆师范大学数学科学学院,新疆乌鲁木齐 830017
- 折叠
摘要
设F是定义在复平面D上的一族亚纯函数,m≥0,n≥2,k≥1为3个正整数.设φ(z)为区域D上零点重数最少为m的解析函数,且φ(z)(≠)0.设P是一个多项式,deg(P)≥3,且至少有一个q重零点,m可被n+q整除.若对任意的f∈F,f的零点重数最少是k+m/q,并且极点重数最少是m+1.则对每一组(f,g)∈F,若P(f)(f(k))n与P(g)(g(k))n分担φ(z),则F在D上正规.
Abstract
Take positives integers m≥ 0,n≥ 2,k≥ 1.Let F be a family of meromorphic functions defined in a domain D.Let φ(z)≠ 0 be an analytic function with zeros of multiplicity m in a domain D.Let P be a polynomial with deg(P)≥ 3 and had at least one q-fold zero,m can be divisible by n+q.For every f ∈ F,f has only zeros with multiplicity at least k+m/q,and all its poles of multiplicity at least m+1.If P(f)(f(k))n and P(g)(g(k))n share φ(z)in D for each pair of(f,g)∈ F,then F is normal in D.
关键词
正规族/分担函数/亚纯函数Key words
normal family/share functions/meromorphic functions引用本文复制引用
出版年
2024
NETL
NSTL
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