Zero distribution of some delay-differential polynomials
Bull. Korean Math. Soc. 2020 Vol. 57, No. 6, 1541-1565
Published online November 2, 2020
Printed November 30, 2020
Ilpo Laine, Zinelaabidine Latreuch
University of Eastern Finland; University of Mostaganem
Abstract : Let $f$ be a meromorphic function of finite order $\rho$ with few poles in the sense $S_{\lambda}(r,f):=O(r^{\lambda +\varepsilon})+S(r,f)$, where $\lambda <\rho$ and $\varepsilon \in (0,\rho-\lambda)$, and let $g(f):=\sum_{j=1}^{k}b_{j}(z)f^{(k_j)}(z+c_{j})$ be a linear delay-differential polynomial of $f$ with small meromorphic coefficients $b_{j}$ in the sense $S_{\lambda}(r,f)$. The zero distribution of $f^{n}(g(f))^{s}-b_{0}$ is considered in this paper, where $b_0$ is a small function in the sense $S_{\lambda}(r,f)$.
Keywords : Meromorphic functions, delay-differential polynomial, shifts, zero distribution
MSC numbers : Primary 30D35
Supported by : The first author has been partially supported by The Academy of Finland project no. 286877. The second author has been supported by the Directorate General for Scientific Research and Technological Development (DGRSDT), Algeria
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