Abstract
The purpose of this paper is mainly to prove that if f is a transcendental entire function of hyper-order strictly less than 1 and \(f(z)^{n}+a_{1}f'(z)+\cdots +a_{k}f^{(k)}(z)\) is a periodic function, then f(z) is also a periodic function, where n, k are positive integers, and \(a_{1},\cdots ,a_{k}\) are constants. Meanwhile, we offer a partial answer to Yang’s Conjecture, theses results extend some previous related theorems.
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The authors would like to thank the referees for their several important suggestions and for pointing out some typos in our original manuscript.
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Lü, W., Zhang, X. On the Periodicity of Entire Functions. Results Math 75, 176 (2020). https://doi.org/10.1007/s00025-020-01302-4
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DOI: https://doi.org/10.1007/s00025-020-01302-4