ON THE DISTRIBUTION OF MEROMORPHIC FUNCTIONS OF POSITIVE HYPER-ORDER

被引：0

作者：

Yang, P. ^{[1
]}

Wang, S. ^{[1
]}

机构：

[1] Chengdu Univ Informat Technol, Coll Appl Math, Chengdu 610225, Peoples R China

来源：

ANALYSIS MATHEMATICA | 2021年 / 47卷 / 01期

基金：

中国国家自然科学基金;

关键词：

meromorphic function; characteristic function; normal family;

D O I：

10.1007/s10476-021-0070-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f(z) be a transcendental meromorphic function, whose zeros have multiplicity at least 3. Set alpha(z): = beta(z)exp (gamma(z), where beta(z) is a nonconstant elliptic function and gamma(z) is an entire function. If sigma(f(z)) > sigma(alpha(z)), then f '(z) = alpha(z) has infinitely many solutions in the complex plane.

引用

页码：243 / 260

页数：18

共 13 条

[1] PICARD VALUES OF MEROMORPHIC FUNCTIONS AND THEIR DERIVATIVES [J].

HAYMAN, WK .

ANNALS OF MATHEMATICS, 1959, 70 (01) :9-42

[2] On the kth derivative of meromorphic functions with zeros of multiplicity at least k+1 [J].

Liu, Xiaojun ;

Nevo, Shahar ;

Pang, Xuecheng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 348 (01) :516-529

[3]

Nevo S, 2001, COMPLEX VAR ELLIPTIC, V46, P315

[4]

Nevo S., 2001, Analysis, V21, P289, DOI [10.1524/anly.2001.21.3.289, DOI 10.1524/ANLY.2001.21.3.289]

[5] Normal families and shared values [J].

Pang, XC ;

Zalcman, L .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2000, 32 :325-331

[6]

Pang XC, 2008, COMPUT METH FUNCT TH, V8, P483, DOI DOI 10.1007/BF03321700

[7]

Tsuji M., 1950, TOHOKU MATH J, V2, P97, DOI [10.2748/tmj/1178245639, DOI 10.2748/TMJ/1178245639]

[8]

Wang YF, 1998, ACTA MATH SIN, V14, P17

[9] Normal families and exceptional functions [J].

Xu, Yan .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (02) :1343-1354

[10] The second main theorem for small functions and related problems [J].

Yamanoi, K .

ACTA MATHEMATICA, 2004, 192 (02) :225-294

← 1 2 →