Uniqueness of entire functions sharing two values with their partial derivative operators

TL;DR

This paper proves new uniqueness theorems for entire functions sharing two values with their partial derivatives using normal family theory in several complex variables.

Contribution

It extends existing uniqueness results to the setting of several complex variables and provides examples demonstrating the sharpness of these theorems.

Findings

Established new uniqueness theorems for entire functions in several complex variables.

Extended prior results of Li and Yi, and Lü et al. to higher dimensions.

Provided examples confirming the sharpness of the theorems.

Abstract

In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of several complex variables. Moreover, some examples are provided to demonstrate the sharpness of our results.