Abstract
We discuss the relationship on the periodicity of a transcendental entire function with its differential polynomials. For example, we obtain that if f is a transcendental entire function, k is a non-negative integer and if (anfn + ⋯ + a1f)(k) is a periodic function, then f is also a periodic function, where a1, … an (≠ 0) are constants. Our results are related to Yang’s Conjecture on the periodicity of transcendental entire functions.
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Acknowledgements
All authors are very grateful to Professor Risto Korhonen and the referee for useful comments for the paper. The present proof of case n ≥ 4 in Theorem 1.1 is provided by Prof. Risto Korhonen. The third author also thanks Prof. Risto Korhonen for his hospitality during the study period in the Department of Physics and Mathematics, University of Eastern Finland.
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This work was partial supported by the NSFC (No. 11661052, 12061042) and the NSF of Jiangxi (No. 20202BAB201003). The third author was also supported by the EDUFI Fellowship (TM-18-11020).
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Wei, Y.M., Liu, K. & Liu, X.L. The Periodicity on a Transcendental Entire Function with its Differential Polynomials. Anal Math 47, 695–708 (2021). https://doi.org/10.1007/s10476-021-0098-2
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DOI: https://doi.org/10.1007/s10476-021-0098-2