On value distribution of certain delay-differential polynomials

IF 1 4区综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES

Scienceasia Pub Date : 2022-05-15 DOI:10.2306/scienceasia1513-1874.2023.010

Nan Li, Lian-Zhong Yang

引用次数: 0

Abstract

Given an entire function $f$ of finite order $\rho$, let $L(z,f)=\sum_{j=0}^{m}b_{j}(z)f^{(k_{j})}(z+c_{j})$ be a linear delay-differential polynomial of $f$ with small coefficients in the sense of $O(r^{\lambda+\varepsilon})+S(r,f)$, $\lambda<\rho$. Provided $\alpha$, $\beta$ be similar small functions, we consider the zero distribution of $L(z,f)-\alpha f^{n}-\beta$ for $n\geq 3$ and $n=2$, respectively. Our results are improvements and complements of Chen(Abstract Appl. Anal., 2011, 2011: ID239853, 1--9), and Laine (J. Math. Anal. Appl. 2019, 469(2): 808--826.), etc.

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一类时滞微分多项式的值分布

给定一个有限阶$\rho$的完整函数$f$，设$L(z,f)=\sum_{j=0}^{m}b_{j}(z)f^{(k_{j})}(z+c_{j})$是$f$的线性延迟微分多项式，具有$O(r^{\lambda+\varepsilon})+S(r,f)$, $\lambda<\rho$意义上的小系数。假设$\alpha$和$\beta$是类似的小函数，我们分别考虑$L(z,f)-\alpha f^{n}-\beta$对$n\geq 3$和$n=2$的零分布。我们的研究结果是对Chen(Abstract，应用)的改进和补充。分析的[j] .数学学报，2011,2011:ID239853, 1—9]。分析的应用科学学报，2019,469(2):808—826。

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来源期刊

Scienceasia MULTIDISCIPLINARY SCIENCES-

CiteScore

1.70

自引率

33.30%

发文量

102

审稿时长

1 months

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