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The Periodicity of Entire Functions with Finite Order

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  • Zhiguo Ren
  • Guoqiang Dang
  • kit C. Chan

Abstract

This paper is concerned with the periodicity of entire functions with finite growth order, and some sufficient conditions are given. Let f is a transcendental entire function with finite growth order, zero is a Picard exceptional value of f, and a given differential monomial Qf of f is periodic, then f is also periodic. We are also interested in finding the following: let f is a transcendental entire function with finite growth order, d is a Picard exceptional value of f and fzΔcnfz is a periodic function, then f is also a periodic function. These results extend Yang’s conjecture.

Suggested Citation

  • Zhiguo Ren & Guoqiang Dang & kit C. Chan, 2021. "The Periodicity of Entire Functions with Finite Order," Journal of Mathematics, Hindawi, vol. 2021, pages 1-8, May.
    • Handle: RePEc:hin:jjmath:9995695
    DOI: 10.1155/2021/9995695
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