与微分多项式分担值相关的正规定则

数学季刊 ›› 2013, Vol. 28 ›› Issue (1): 87-92.

与微分多项式分担值相关的正规定则

1. South China Institute of Software Engineering, Guangzhou University 2. Institute of Applied Mathematics, South China Agricultural University

收稿日期:2011-06-21 出版日期:2013-03-30 发布日期:2023-03-08
作者简介:DENG Bing-mao(1985-), male, native of Jieyang, Guangdong, a student of South China Agricultural University, M.S.D., engages in complex analysis.
基金资助:
Supported by the NNSF of China(11071083)； Supported by the National Natural Science Foundation of Tianyuan Foundation(11126267)

Normality and Shared Value Concerning Differential Polynomials

1. South China Institute of Software Engineering, Guangzhou University 2. Institute of Applied Mathematics, South China Agricultural University

Received:2011-06-21 Online:2013-03-30 Published:2023-03-08
About author:DENG Bing-mao(1985-), male, native of Jieyang, Guangdong, a student of South China Agricultural University, M.S.D., engages in complex analysis.
Supported by:
Supported by the NNSF of China(11071083)； Supported by the National Natural Science Foundation of Tianyuan Foundation(11126267)

摘要/Abstract

摘要： Let F be a family of functions meromorphic in a domain D, let m, n_k, k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for each f∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F, P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and n_k≥max_1≤i≤k-1{n_i}; (3) m ≥ 2 or n_k≥ 2, k ≥ 2, then F is normal in D.

关键词: meromorphic function, normality, shared value

Abstract: Let F be a family of functions meromorphic in a domain D, let m, n_k, k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for each f∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F, P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and n_k≥max_1≤i≤k-1{n_i}; (3) m ≥ 2 or n_k≥ 2, k ≥ 2, then F is normal in D.

Key words:

meromorphic function, normality, shared value

中图分类号:

O174.5

邓炳茂, 雷春林, 杨德贵. 与微分多项式分担值相关的正规定则[J]. 数学季刊, 2013, 28(1): 87-92.

DENG Bing-mao, LEI Chun-lin, YANG De-gui. Normality and Shared Value Concerning Differential Polynomials[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(1): 87-92.

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