On the value distribution of differential polynomials of meromorphic functions

Yan Xu¹ ; Huiling Qiu²

¹ Department of Mathematics Nanjing Normal University Nanjing 210046, P.R. China
² Department of Applied Mathematics Nanjing Audit University Nanjing 210029, P.R. China

Annales Polonici Mathematici, Tome 98 (2010) no. 3, pp. 283-289

Résumé

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.

Détail

DOI : 10.4064/ap98-3-7

Keywords: transcendental meromorphic function infinite order mathbb mathbb varphi where equiv rational function polynomial ldots k holomorphic functions mathbb zeros have multiplicity least except possibly finitely many leftrightarrow k k cdots k k cdots f varphi has infinitely many zeros