涉及微分多项式分担函数的正规定则

数学物理学报 ›› 2018, Vol. 38 ›› Issue (2): 222-230.

涉及微分多项式分担函数的正规定则

邓炳茂, 雷春林, 方明亮

华南农业大学应用数学研究所广州 510642

收稿日期:2017-02-17 修回日期:2017-09-06 出版日期:2018-04-26 发布日期:2018-04-26
通讯作者: 方明亮 E-mail:mlfang@scau.edu.cn
作者简介:邓炳茂,E-mail:dbmao2012@163.com;雷春林,E-mail:leichunlin0113@126.com
基金资助:
国家自然科学基金（11371149）和华南农业大学博士生国外联合培养（2017LHPY003）

Normality and Shared Function Concerning Differential Polynomials

Deng Bingmao, Lei Chunlin, Fang Mingliang

Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642

Received:2017-02-17 Revised:2017-09-06 Online:2018-04-26 Published:2018-04-26
Supported by:
Supported by the NSFC (11371149) and the Graduate Student Overseas Study Program from South China Agricultural University (2017LHPY003)

摘要/Abstract

摘要： 设m（≥ 0）是一个正整数，h（z）（≢0）是区域D内的全纯函数，且其零点重级均≤ m，P是多项式满足deg P ≥ 3，或者deg P=2且P仅有一个零点.设F是区域D内的一族亚纯函数，其零点与极点重级均≥ m+1.如果对于F中的任意两个函数f，g，P（f）f'与P（g）g'分担h（z），则F在区域D内正规.该结果改进了Lei and Fang^[8]，Zhang^[16]等人的结果.

关键词: 亚纯函数, 正规定则, 分担函数

Abstract: Let m(≥ 0) be an integer, let h(z)(≢0) be a holomorphic function in a domain D with all zeros have multiplicity at most m, let P be a polynomial with either deg P ≥ 3 or deg P=2 and P having only one distinct zero, and let F be a family of meromorphic functions in a domain D, all of whose zeros and poles have multiplicity at least m+1. If, for each pair of functions f and g in F, P(f)f' and P(g)g' share h(z) in D, then F is normal in D. The result improved the results due to Lei and Fang^[8], Zhang^[16].

Key words: Meromorphic function, Normal criterion, Shared function

中图分类号:

O174.5

邓炳茂, 雷春林, 方明亮. 涉及微分多项式分担函数的正规定则[J]. 数学物理学报, 2018, 38(2): 222-230.

Deng Bingmao, Lei Chunlin, Fang Mingliang. Normality and Shared Function Concerning Differential Polynomials[J]. Acta mathematica scientia,Series A, 2018, 38(2): 222-230.

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