Uniqueness of entire function concerning derivatives and shifts

2025/10/11 by Sujoy Majumder, Nabadwip Sarkar, Majumder, Sujoy +1
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Primary 30D35 #Secondary 34A20

paper · pdf · doi:10.48550/arxiv.2510.10275

openalex publication_date 2025/10/11 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

In the paper, we investigate the uniqueness problem of entire function concerning its derivative and shift and obtain two results. On of our result solves the open problem posed by Majumder et al. (On a conjecture of Li and Yang, Hiroshima Math. J., 53 (2023), 199-223) and the other result improves and generalizes the recent result due to Huang and Fang (Unicity of entire functions concerning their shifts and derivatives, Comput. Methods Funct. Theory, 21 (2021), 523-532) in a large extend.

Citations

• Holomorphic curves with shift-invariant hyperplane preimages
• On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane
• When an entire function and its linear differential polynomial share two values

Related

• Uniqueness of entire functions concerning their linear differential polynomials in shift
• Value sharing by an entire function with its derivatives
• Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation
• Uniqueness of differential polynomials sharing one value
• Partial sharing and cross sharing of entire function with its derivative