A Uniqueness Problem Concerning Entire Functions and Their Derivatives

被引：0

作者：

Sauer, Andreas ^{[1
]}

Schweizer, Andreas ^{[2
]}

机构：

[1] Hsch Ruhr West, Duisburger Str 100, D-45479 Mulheim, Germany

[2] Kongju Natl Univ, Dept Math Educ, Gongju 32588, South Korea

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2024年 / 24卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Entire function; Shared value; Uniqueness problem; Differential equation; Periodic function; Normality; MEROMORPHIC FUNCTIONS; NORMAL-FAMILIES; VALUES;

D O I：

10.1007/s40315-023-00486-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We determine all entire functions f such that for non-zero complex values a not equal b the implications f = a double right arrow f ' = a and f ' = b double right arrow f = b hold. This solves an open problem in uniqueness theory. In this context, we give a normality criterion, which might be interesting in its own right.

引用

页码：163 / 183

页数：21

共 12 条

[1]

Ahlfors L.V., 1979, COMPLEX ANAL

[2]

Cherry W., 2001, Nevanlinna theory of value distribution, DOI [10.1007/978-3-662-12590-8, DOI 10.1007/978-3-662-12590-8]

[3]

CLUNIE J, 1966, COMMENT MATH HELV, V40, P117

[4] MEROMORPHIC FUNCTIONS THAT SHARE FINITE VALUES WITH THEIR DERIVATIVE [J].

GUNDERSEN, GG .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1980, 75 (02) :441-446

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

HAYMAN, WK .

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

[6]

Lehto O., 1957, ANN ACAD SCI FENN A1

[7] Normal families and uniqueness of entire functions and their derivatives [J].

Li, Jiangtao ;

Yi, Hongxun .

ARCHIV DER MATHEMATIK, 2006, 87 (01) :52-59

[8] Uniqueness theorems and normal families of entire functions and their derivatives [J].

Lue, Feng ;

Xu, Junfeng ;

Yi, Hongxun .

ANNALES POLONICI MATHEMATICI, 2009, 95 (01) :67-75

[9] MEROMORPHIC FUNCTIONS SHARING VALUES WITH THEIR DERIVATIVE [J].

MUES, E ;

STEINMETZ, N .

MANUSCRIPTA MATHEMATICA, 1979, 29 (2-4) :195-206

[10]

Ostrowski A., 1924, MATH Z, V24, P215, DOI [10.1007/BF01216780, DOI 10.1007/BF01216780]

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