Year: 2020
Type: preprint
Abstract: In this paper, we study a problem of non-constant entire function $ f $ that shares a set $ \mathcal{S}=\{a,b,c\} $ with its $ k $-th derivative $ f^{(k)} $, where $ a, b $ and $ c $ are any three distinct complex numbers. We have found a gap in the statement of the main result of \textit{Chang-Fang-Zalcman} \cite{Cha & Fan & al-ADM-2007} and with some help of the method used by \textit{Chang-Fang-Zalcman}, we have generalized the result of \textit{Chang-Fang-Zalcman} in a more compact form. As an application, we generalize the famous Br$\ddot{u}$ck conjecture \cite{Bru-1996} with the idea of set sharing.
Source: arXiv (Cornell University)
Author: Ahamed, Molla Basir
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4287862443