Rigidity of entire functions sharing a finite set with their partial derivatives in C^n
Complex Variables
2026-04-01 v1
Abstract
This paper investigates certain classes of entire functions in C^n that, together with their partial derivatives, share a finite set consisting of three elements. By employing normality criteria, we study the behaviour of such functions and derive the necessary conditions governing their existence. Our results extend those of [4], originally established for functions of a single complex variable, to the setting of several complex variables, thereby providing a comprehensive generalization of the earlier result in a direction not previously explored.
Cite
@article{arxiv.2603.29412,
title = {Rigidity of entire functions sharing a finite set with their partial derivatives in C^n},
author = {Sujoy Majumder and Abhijit Banerjee and Shantanu Panja},
journal= {arXiv preprint arXiv:2603.29412},
year = {2026}
}