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arXiv · 2603.12190

A normality criterion for a family of meromorphic functions

Kuntal Mandal·Bipul Pal
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Abstract

We consider a family $\mathscr{F}$ of meromorphic functions defined in a domain $D$, a holomorphic function $ψ$ and a homogeneous differential polynomial $ P[f] $ of degree $d$ with weight $w$. In this paper, we prove the normality of $\mathscr{F}$ under certain conditions such as $f\neq 0$, $P[f]\neq 0$ and all the zeros of the function $P[f] - ψ^d$ have multipicity at least $\displaystyle{\frac{w+1}{w-1}}$, for each $f \in \mathscr{F}$.

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Kuntal Mandal, Bipul Pal. 2026-03-12. A normality criterion for a family of meromorphic functions. https://arxiv.org/abs/2603.12190

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