Uniqueness of meromorphic function sharing three small functions CM with its n- exact difference

2021/03/03 by XiaoHuang Huang, Huang, XiaoHuang
Mathematics · #30D35 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2103.06235

openalex publication_date 2021/03/03 · openalex created_date 2021/03/15 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the uniqueness of the difference of meromorphic functions. We prove the following result: Let f be a non-constant meromorphic function of hyper-order less than 1, let η be a non-zero complex number, n≥1, an integer, and let a,b,c∈S(f) be three distinct small functions and two of them be periodic small functions with period η. If f and Δ_ηⁿf share a,b,c CM, then f≡Δ_ηⁿf.

Citations

• Meromorphic Functions that Share Three or Four Values

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