Paired Hayman conjecture and uniqueness of complex delay-differential polynomials

Bull. Korean Math. Soc. Published online November 1, 2021

Yingchun Gao and Kai Liu
Nanchang University; Nanchang University

Abstract : 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 differential operator $h^{(k)}(z)$ or shift operator $h(z+c)$ or difference operator $h(z+c)-h(z)$ or delay-differential operator $h^{(k)}(z+c)$, 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.