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Research articles

ScienceAsia 48 (2022):ID 759-763 |doi: 10.2306/scienceasia1513-1874.2022.097

The periodicity on a transcendental entire function with its differential-difference polynomials

Yong Liua,b,*, Shuai Jianga

ABSTRACT:     According to a conjecture by C. C. Yang [Houston J Math 45 (2019):431?437], if ?(z)?(k) (z) is a periodic function, where ?(z) is a transcendental entire function and k is a positive integer, then ?(z) is also a periodic function. We consider the related questions, which can be viewed as differential-difference versions of Yang?s conjecture. We discuss the periodicity of a transcendental entire function ?(z) when differential-difference polynomials in ?(z) are periodic.

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a Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000 China
b College of Science, Ningbo University of Technology, Ningbo, Zhejiang 315211 China

* Corresponding author, E-mail: liuyongsdu@aliyun.com

Received 8 Sep 2021, Accepted 13 Apr 2022