The Periodicity of Entire Functions with Finite Order

This paper is concerned with the periodicity of entire functions with finite growth order, and some sufficient conditions are given. Let f is a transcendental entire function with finite growth order, zero is a Picard exceptional value of f, and a given differential monomial Qf of f is periodic, the...

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Main Authors: Zhiguo Ren, Guoqiang Dang
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/9995695
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author Zhiguo Ren
Guoqiang Dang
author_facet Zhiguo Ren
Guoqiang Dang
author_sort Zhiguo Ren
collection DOAJ
description This paper is concerned with the periodicity of entire functions with finite growth order, and some sufficient conditions are given. Let f is a transcendental entire function with finite growth order, zero is a Picard exceptional value of f, and a given differential monomial Qf of f is periodic, then f is also periodic. We are also interested in finding the following: let f is a transcendental entire function with finite growth order, d is a Picard exceptional value of f and fzΔcnfz is a periodic function, then f is also a periodic function. These results extend Yang’s conjecture.
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institution Kabale University
issn 2314-4629
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publishDate 2021-01-01
publisher Wiley
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spelling doaj-art-7632f45d0125426c8fed3ffac7b9b0a42025-02-03T06:06:28ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99956959995695The Periodicity of Entire Functions with Finite OrderZhiguo Ren0Guoqiang Dang1Department of Education and Educational Technology, Jiangmen Polytechnic, Jiangmen 529090, Guangdong, ChinaSchool of Mathematical Sciences, Beijing Normal University, Beijing 100875, ChinaThis paper is concerned with the periodicity of entire functions with finite growth order, and some sufficient conditions are given. Let f is a transcendental entire function with finite growth order, zero is a Picard exceptional value of f, and a given differential monomial Qf of f is periodic, then f is also periodic. We are also interested in finding the following: let f is a transcendental entire function with finite growth order, d is a Picard exceptional value of f and fzΔcnfz is a periodic function, then f is also a periodic function. These results extend Yang’s conjecture.http://dx.doi.org/10.1155/2021/9995695
spellingShingle Zhiguo Ren
Guoqiang Dang
The Periodicity of Entire Functions with Finite Order
Journal of Mathematics
title The Periodicity of Entire Functions with Finite Order
title_full The Periodicity of Entire Functions with Finite Order
title_fullStr The Periodicity of Entire Functions with Finite Order
title_full_unstemmed The Periodicity of Entire Functions with Finite Order
title_short The Periodicity of Entire Functions with Finite Order
title_sort periodicity of entire functions with finite order
url http://dx.doi.org/10.1155/2021/9995695
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