On the value distribution of differential polynomials of meromorphic functions
Volume 98 / 2010
Annales Polonici Mathematici 98 (2010), 283-289
MSC: Primary 30D35.
DOI: 10.4064/ap98-3-7
Abstract
Let $f$ be a transcendental meromorphic function of infinite order on $\mathbb{C}$, let $k\in \mathbb{N}$ and $\varphi=Re^P$, where $R\not\equiv 0$ is a rational function and $P$ is a polynomial, and let $a_0, a_1, \ldots, a_{k-1}$ be holomorphic functions on $\mathbb{C}$. If all zeros of $f$ have multiplicity at least $k$ except possibly finitely many, and $f=0\Leftrightarrow f^{(k)}+a_{k-1}f^{(k-1)}+\cdots+a_0f=0$, then $f^{(k)}+a_{k-1}f^{(k-1)}+\cdots+a_0f-\varphi$ has infinitely many zeros.
