Zero Distribution on Differential-Difference Polynomials of Exponential Type Functions

被引：3

作者：

Liu, Kai ^{[1
]}

Gao, Linkui ^{[1
]}

Liu, Xinling ^{[1
,2
]}

机构：

[1] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

[2] Univ Eastern Finland, Dept Math & Phys, POB 111, Joensuu 80101, Finland

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2019年 / 19卷 / 04期

关键词：

Exponential polynomials; Differential-difference polynomials; Value distribution;

D O I：

10.1007/s40315-019-00290-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Exponential type functions are important subclasses of transcendental entire functions. In this paper, we will use some results given by Steinmetz (Manuscr Math 26:155-167, 1978) to consider the zeros of difference or differential-difference polynomials of exponential polynomials. In addition, we also consider the zeros of difference polynomials of exponential type functions with infinite order.

引用

页码：717 / 728

页数：12

共 18 条

[1] Chen ZX, 2014, MATH MONOGRAPH SERIE
[2] On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane
Chiang, Yik-Man
Feng, Shao-Ji
[J]. RAMANUJAN JOURNAL, 2008, 16 (01) : 105 - 129
[3] Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations
Halburd, RG
Korhonen, RJ
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 314 (02) : 477 - 487
[4] HOLOMORPHIC CURVES WITH SHIFT-INVARIANT HYPERPLANE PREIMAGES
Halburd, Rodney
Korhonen, Risto
Tohge, Kazuya
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (08) : 4267 - 4298
[5] Hayman W. K., 1964, Meromorphic Functions
[6] PICARD VALUES OF MEROMORPHIC FUNCTIONS AND THEIR DERIVATIVES
HAYMAN, WK
[J]. ANNALS OF MATHEMATICS, 1959, 70 (01) : 9 - 42
[7] Laine I, 1993, NEVANLINNA THEORY CO
[8] Value distribution of difference polynomials
Laine, Ilpo
Yang, Chung-Chun
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2007, 83 (08) : 148 - 151
[9] Zero distribution of some shift polynomials
Laine, Ilpo
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 469 (02) : 808 - 826
[10] On Picard value problem of some difference polynomials
Latreuch Z.
Belaïdi B.
[J]. Arabian Journal of Mathematics, 2018, 7 (1) : 27 - 37

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