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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.
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참고문헌 (17)
참고문헌 신청
I. N. Baker / 1966 / On some results of A. Renyi and C. Renyi concerning periodic entire functions / Acta Sci. Math. (Szeged) 27:197~200
X. J. Dong / 2019 / Structure of entire solutions to general linear differential-difference equa-tions with constant coefficients / Houston. J. Math 45(4):1021~1036
Fred Gross / 1972 / On periodic entire functions / Rendiconti del Circolo Matematico di Palermo 21(3):284~292
G. Halász / 1972 / On the periodicity of composed integral functions / Periodica Mathematica Hungarica 2(1-4):73~83
J. Heittokangas / 2009 / Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity / Journal of Mathematical Analysis and Applications 355(1):352~363
X. J. Dong / 2019 / Structure of entire solutions to general linear differential-difference equa-tions with constant coefficients / Houston. J. Math 45(4):1021~1036
Fred Gross / 1972 / On periodic entire functions / Rendiconti del Circolo Matematico di Palermo 21(3):284~292
G. Halász / 1972 / On the periodicity of composed integral functions / Periodica Mathematica Hungarica 2(1-4):73~83
J. Heittokangas / 2009 / Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity / Journal of Mathematical Analysis and Applications 355(1):352~363
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