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<p>A fundamental observation reveals that if <i>f</i>(<i>z</i>) is a periodic meromorphic function, then all complex differential polynomials in <i>f</i>(<i>z</i>) with constant coefficients inherently inherit the periodicity. The inverse problem, however, remains challenging to resolve, as exemplified by Yang’s conjecture which is an open question under active investigation in recent studies. In this paper, we figure out the periodicity of <i>f</i>(<i>z</i>) when its complex differential polynomial of a specific type exhibits periodicity.</p>

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Periodicity of Complex Differential Polynomials with Specific Type

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Xinling Liu,
  • Jun Wang

摘要

A fundamental observation reveals that if f(z) is a periodic meromorphic function, then all complex differential polynomials in f(z) with constant coefficients inherently inherit the periodicity. The inverse problem, however, remains challenging to resolve, as exemplified by Yang’s conjecture which is an open question under active investigation in recent studies. In this paper, we figure out the periodicity of f(z) when its complex differential polynomial of a specific type exhibits periodicity.