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On the value distribution of differential polynomials of meromorphic functions

Tom 98 / 2010

Annales Polonici Mathematici 98 (2010), 283-289 MSC: Primary 30D35. DOI: 10.4064/ap98-3-7

Streszczenie

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.

Autorzy

• Yan XuDepartment of Mathematics
Nanjing Normal University
Nanjing 210046, P.R. China
e-mail
• Huiling QiuDepartment of Applied Mathematics
Nanjing Audit University
Nanjing 210029, P.R. China
e-mail

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