Bulletin of the
Korean Mathematical Society BKMS

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).