A Note on the value distribution of some differential-difference monomials generated by a transcendental entire function of hyper-order less than one

2025/01/24 by Soumon Roy, Roy, Soumon, Sudip Saha +3
Computer Science · Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Meromorphic and Entire Functions #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2501.14839

openalex publication_date 2025/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathfrakf be a transcendental entire function with hyper-order less than one. The aim of this note is to study the value distribution of the differential-difference monomials α\mathfrakf(z)^q₀(\mathfrakf(z+c))^q₁, where c is a non-zero complex number and q₀≥2, q₁≥ 1 are non-negative integers, and α(z) (\not≡ 0,∞) be a small function of \mathfrakf.

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