Uniqueness of power of a meromorphic function with its differential polynomial

TL;DR

This paper advances the understanding of meromorphic functions by proving a new theorem that extends recent results related to the Brück Conjecture, focusing on the uniqueness of a function's power in relation to its differential polynomial.

Contribution

The paper introduces a new theorem that improves and extends existing results on the uniqueness of meromorphic functions with their differential polynomials, addressing questions posed by Zhang and Lü.

Findings

Established a new theorem improving previous results

Extended the scope of the Brück Conjecture

Provided insights into the uniqueness of meromorphic functions

Abstract

In this paper, taking the question of Zhang and L\"{u} into the background, we present one theorem which will improve and extend some recent results related to the Br\"{u}ck Conjecture.