分担集合的正规亚纯函数  

Normal Function Related to Shared Sets

作　　者：黄小杰[1,2] 刘芝秀[1] 李运通 Huang Xiaojie;Liu Zhixiu;Li Yuntong(Department of Science,Nanchang Institute of Technology,Nanchang 330099,China;School of Mathematic Sciences,Fudan University,Shanghai 200433,China;Shanxi Railway Institute,Weinan 714000,China)

机构地区：[1]南昌工程学院理学院,江西南昌330099 [2]复旦大学数学科学学院,上海杨浦200433 [3]陕西铁路职业技术学院,陕西渭南714000

出　　处：《南京师大学报（自然科学版）》2018年第4期12-18,共7页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11671091;11771090);上海市自然科学基金(17ZR1402900);陕西省教育厅专项基金(17JK0170);江西省教育厅科技项目(GJJ180944)

摘　　要：研究了涉及函数与其高阶导数分担集合的亚纯函数正规条件,利用Lohwater-Pommerenke定理和Zalcman-Pang引理以及Nevanlinna理论证明了如下结论,设S_1={a_1,a_2,a_3}和S_2={b1,b2}是由互异有限复数构成的集合,k≥2是一个正整数,f(z)是单位圆Δ内的亚纯函数,如果f(z)-a_i的零点重数都至少为k,i=1,2,3,且{z∈Δ|f(z)∈S_1}={z∈Δ|f^(k)(z)∈S_2},那么f(z)是Δ上的正规函数.This paper studies the normal conditions of meromorphic function relating to sharing sets by the function and its higher derivatives.By use of Lohwater-Pommerenke’s theorem and Zalcman-Pang’s lemma as well as Nevanlinna theory,it proves that let S1={a1,a2,a3} and S 2={b1,b2} be two sets consisting of different finite complex numbers,k≥2 be a positive integer number,if f(z) be a meromorphic function on unit circle domain Δ such that the zeros of f(z)-a i have multiplicity at least k,i=1,2,3 and {z∈Δ|f(z)∈S1}={z∈Δ|f^(k)(z)∈S2},then f(z) is a normal function on domain Δ.

关 键 词：正规函数 正规族 分担集合 

分 类 号：O174.5[理学—数学]