Unicity on meromorphic function sharing three small functions CM with its higher-order difference operators

2021/05/10 by XiaoHuang Huang, Huang, XiaoHuang
Mathematics · #30D35 #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2106.08958

openalex publication_date 2021/05/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the uniqueness of the shift of meromorphic functions. We prove: Let f be a non-constant meromorphic function satisfying ρ₂(f)<1, let η be a non-zero complex number, and let a,b,c∈S(f) be three distinct small functions. If f and Δⁿ_ηf share a,b,c CM, then f≡ Δⁿ_ηf.

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