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arXiv · 2603.29412

Rigidity of entire functions sharing a finite set with their partial derivatives in C^n

Sujoy Majumder·Abhijit Banerjee·Shantanu Panja
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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.

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Sujoy Majumder, Abhijit Banerjee, Shantanu Panja. 2026-03-31. Rigidity of entire functions sharing a finite set with their partial derivatives in C^n. https://arxiv.org/abs/2603.29412

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