Generalized Yang's Conjecture on the periodicity of entire functions
Bull. Korean Math. Soc.
Published online March 3, 2020
Kai Liu, Yuming Wei, and Peiyong Yu
Nanchang University
Abstract : On the periodicity of transcendental entire functions, Yang's Conjecture is proposed in [7,14]. In the paper, we mainly consider and obtain partial results on a general version of Yang's Conjecture, namely, if $f(z)^{n}f^{(k)}(z)$ is a periodic function, then $f(z)$ is also a periodic function. In addition, we prove that if $f(z)^{n}+f^{(k)}(z)$ is a periodic function, then $f(z)$ is also a periodic function, where $n,k$ are positive integers.
Keywords : Entire functions; Periodicity; Differential-difference equations.
MSC numbers : 30D35, 39A05.
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd