Uniqueness of entire function and its linear differential polynomial

Abstract

In this paper we investigate the uniqueness problem of entire function \(f\) and its linear differential polynomial
\begin{equation*}
a_{k}\left( z\right) f^{\left( k\right) }+a_{k-1}\left( z\right) f^{\left(k-1\right) }+\cdots+a_{1}\left( z\right) f'
\end{equation*}
sharing an entire function \(a\equiv a\left( z\right)\) counting multiplicities(CM) with
\begin{equation*}
\sigma \left( a\right) <\sigma \left( f\right)
\end{equation*}
under some restrictions imposed on the coefficients \(a_{j}\left( z\right) \left( {j=1,2,\dots,k}\right)\). Our result improves and generalizes some earlier results.