Power of a meromorphic function sharing value with its k-th order directional derivative in C^m

Abjijit Banerjee; Sujoy Majumder; Debabrata Pramanik

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arXiv · 2511.01637

Power of a meromorphic function sharing value with its k-th order directional derivative in C^m

Abjijit Banerjee·Sujoy Majumder·Debabrata Pramanik

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Abstract

In the context of several complex variables, we investigate the uniqueness problem for a power of a meromorphic function that shares a value with its $k$-th order directional derivative in $\mathbb{C}^m$. Our results extend previous uniqueness theorems from the one-variable case to higher dimensions. Furthermore, we provide numerous examples to demonstrate that our results are, in certain senses, best possible.

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Abjijit Banerjee, Sujoy Majumder, Debabrata Pramanik. 2025-11-03. Power of a meromorphic function sharing value with its k-th order directional derivative in C^m. https://arxiv.org/abs/2511.01637

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