Uniqueness of Some Differential Polynomials of Meromorphic Functions

TL;DR

This paper advances the understanding of the uniqueness of differential polynomials of meromorphic functions and offers new value distribution results, partially addressing longstanding conjectures in complex analysis.

Contribution

It improves and generalizes previous uniqueness theorems and provides a new value distribution result related to derivatives of meromorphic functions.

Findings

Enhanced uniqueness theorems for differential polynomials

A new value distribution result for derivatives of meromorphic functions

Partial resolution of a conjecture by Fang and Wang

Abstract

In this paper, we prove some uniqueness results which improve and generalize several earlier works. Also, we prove a value distribution result concerning $f^{(k)}$ which provides a partial answer to a question of Fang and Wang [A note on the conjectures of Hayman, Mues and Gol'dberg, Comp. Methods, Funct. Theory (2013)13, 533-543].