Normal families and multiple values

被引：13

作者：

Fang, M. L. ^{[1
]}

Chang, J. M.

机构：

[1] S China Agr Univ, Inst Appl Math, Guangzhou 510642, Peoples R China

[2] Changshu Inst Technol, Dept Math, Jiangsu 215500, Peoples R China

来源：

ARCHIV DER MATHEMATIK | 2007年 / 88卷 / 06期

基金：

中国国家自然科学基金;

关键词：

meromorphic function; normal families; multiplicity;

D O I：

10.1007/s00013-007-1749-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F be a family of meromorphic functions in a domain D, and let k be a positive integer, and let b be a nonzero complex number. If, for each f is an element of F, f not equal 0, f((k)) not equal 0 and the zeros of f((k)) - b have multiplicity at least 3 for k = 1 and 2 for k >= 2, then F is normal in D. Examples show that the multiplicity of the zeros of f((k)) - b is best possible.

引用

页码：560 / 568

页数：9

共 10 条

[1]

CHEN H, 1993, SCI CHINA SER A, V36, P674

[2]

Cu Y. X., 1979, SCI SINICA MATH, P267

[3]

FAN XH, 2000, J E CHINA NORMAL U N, V2, P18

[4]

GU YX, 1978, SCI SINICA, V4, P374

[5]

HAYMAN WK, 1964, MEROMORPHIC FUNCTION

[6]

HUANG J, 1994, J E CHIN NORM U NAT, V3, P23

[7]

Schiff J.L., 1993, Normal Families

[8]

YANG L, 1991, SCI CHINA SER A, V34, P157

[9]

Yang L., 1993, VALUE DISTRIBUTION T

[10] Normal families: New perspectives [J].

Zalcman, L .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 35 (03) :215-230

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