Power of a meromorphic function sharing value with its k-th order directional derivative in C^m
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917056744521728 |
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| author | Banerjee, Abjijit Majumder, Sujoy Pramanik, Debabrata |
| author_facet | Banerjee, Abjijit Majumder, Sujoy Pramanik, Debabrata |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power of a meromorphic function sharing value with its k-th order directional derivative in C^m Banerjee, Abjijit Majumder, Sujoy Pramanik, Debabrata Complex Variables 32A20, 32A22 and 32H30 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. |
| title | Power of a meromorphic function sharing value with its k-th order directional derivative in C^m |
| topic | Complex Variables 32A20, 32A22 and 32H30 |
| url | https://arxiv.org/abs/2511.01637 |