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Normality Criterion Concerning Total Derivatives of Holomorphic Functions in \( {\mathbb {C}}^n \)

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Abstract

This paper continues investigation of conditions involving values shared by holomorphic functions and their total derivatives which imply the normality for a family of holomorphic functions concerning the total derivatives in \( {\mathbb {C}}^n \). Consequently, we obtain normality criterion of a family \( {\mathcal {F}} \) of holomorphic functions f, where each function shares complex values with their linear total differential polynomials \( L_D^k(f) \) in \( {\mathbb {C}}^n \).

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Acknowledgements

The authors express their gratitude to the referee for the helpful suggestions and insightful comments aimed at improving the exposition of the paper.

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  1. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, 700032, India

    Molla Basir Ahamed & Sanju Mandal

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  1. Molla Basir Ahamed
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Correspondence to Molla Basir Ahamed.

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Communicated by Walter Bergweiler.

Dedicated to the memory of Lawrence Zalcman.

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The first author is supported by SERB, SUR/2022/002244, Govt. India. The second author is supported by CSIR-SRF (File No: 09/0096(12546)/2021-EMR-I, dated: 18/12/2023), Govt. of India, New Delhi.

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Ahamed, M.B., Mandal, S. Normality Criterion Concerning Total Derivatives of Holomorphic Functions in \( {\mathbb {C}}^n \). Comput. Methods Funct. Theory (2024). https://doi.org/10.1007/s40315-024-00523-w

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