Uniqueness of entire functions sharing two pairs of values with its difference operator

2021/07/27 by XiaoHuang Huang, Huang, XiaoHuang
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2109.15183

openalex publication_date 2021/07/27 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the sharing values problem that entire function f(z) and its first order difference operator Δ_ηf(z) share two distinct pairs of finite values IM. We prove: Let f(z) be a non-constant entire function of hyper-order less than 1, let η be a non-zero complex number, and let a be a nonzero finite number. Then there exists no such entire function so that f(z) and Δ_ηf(z) share (0,0) and (a,-a) IM. Furthermore, using a result in Wang-Chen-Hu \citewch, we obtain some uniqueness results that when f(z) and Δ_ηf(z) share a≠0 and -a IM.

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