On the uniqueness problems of entire functions and their linear differential polynomials

TL;DR

This paper investigates the uniqueness of transcendental entire functions sharing a non-zero polynomial with their derivatives and linear differential polynomials, extending previous results in the field.

Contribution

It introduces new conditions under which a transcendental entire function sharing a polynomial with its derivatives and linear differential polynomials is unique.

Findings

Established new uniqueness theorems for entire functions sharing polynomials

Extended previous results to include linear differential polynomials with rational coefficients

Provided conditions for the uniqueness of functions sharing a polynomial with derivatives

Abstract

The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a transcendental entire function f that shares a non-zero polynomial a with f', together with its linear differential polynomials of the form with rational function coefficients.