Generalized Yang's Conjecture on the periodicity of entire functions
Bull. Korean Math. Soc. 2020 Vol. 57, No. 5, 1259-1267
Published online September 30, 2020
Kai Liu, Yuming Wei, Peiyong Yu
Nanchang University; Nanchang University; Nanchang University
Abstract : On the periodicity of transcendental entire functions, Yang's Conjecture is proposed in \cite{lilvyang, wanghu}. 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. We also prove that if $f(z)^{n}+f^{(k)}(z)$ is a periodic function with additional assumptions, then $f(z)$ is also a periodic function, where $n,k$ are positive integers.
Keywords : Entire functions, periodicity, differential-difference equations
MSC numbers : Primary 30D35, 39A05
Supported by : This work was partially supported by the NSFC (No.11661052), the outstanding youth scientist foundation plan of Jiangxi (No. 20171BCB23003)
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