Rigidity of entire functions sharing a finite set with their partial derivatives in C^n
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908924673785856 |
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| author | Majumder, Sujoy Banerjee, Abhijit Panja, Shantanu |
| author_facet | Majumder, Sujoy Banerjee, Abhijit Panja, Shantanu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29412 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity of entire functions sharing a finite set with their partial derivatives in C^n Majumder, Sujoy Banerjee, Abhijit Panja, Shantanu Complex Variables 32A19, 32A22 and 32H30 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. |
| title | Rigidity of entire functions sharing a finite set with their partial derivatives in C^n |
| topic | Complex Variables 32A19, 32A22 and 32H30 |
| url | https://arxiv.org/abs/2603.29412 |