Bull. Korean Math. Soc. 2022; 59(1): 155-166
Online first article November 1, 2021 Printed January 31, 2022
https://doi.org/10.4134/BKMS.b210170
Copyright © The Korean Mathematical Society.
Yingchun Gao, Kai Liu
Nanchang University; Nanchang University
In this paper, the paired Hayman conjecture of different types are considered, namely, the zeros distribution of $f(z)^{n}L(g)-a(z)$ and $g(z)^{n}L(f)-a(z)$, where $L(h)$ takes the derivatives $h^{(k)}(z)$ or the shift $h(z+c)$ or the difference $h(z+c)-h(z)$ or the delay-differential $h^{(k)}(z+c)$, where $k$ is a positive integer, $c$ is a non-zero constant and $a(z)$ is a non-zero small function with respect to $f(z)$ and $g(z)$. The related uniqueness problems of complex delay-differential polynomials are also considered.
Keywords: Paired Hayman conjecture, uniqueness, meromorphic functions, Delay-differential polynomials
MSC numbers: Primary 30D35, 39A05
Supported by: This work was partially supported by the NSFC (No.12061042) and the Natural Science Foundation of Jiangxi (No. 20202BAB201003).
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