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

2025/11/03 by Banerjee, Abjijit, Majumder, Sujoy, Pramanik, Debabrata
#32A20 #32A22 and 32H30 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.01637

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 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.

Citations

• A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables

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