Bulletin of the
Korean Mathematical Society BKMS

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)