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On Hayman Conjecture for Paired Complex Delay-Differential Polynomials | | Nidhi Gahlian
; Garima Pant
; | | Date: |
23 Aug 2022 | | Abstract: | We study Hayman conjecture for different paired complex polynomials under
certain conditions. In 2021, the zeros distribution of $f^{n}(z)L(g)-a(z)$ and
$g^{n}(z)L(f)-a(z)$ was studied by Gao and Liu for $ngeq 3$. In this paper, we
work on the zeros distribution of $f^{2}(z)L(g)-a(z)$ and $g^{2}(z)L(f)-a(z)$,
where $a(z)$ is a non-zero small function of both $f(z)$ and $g(z)$, and $L(h)$
takes the $k$th derivative $h^{(k)}(z)$ or shift $h(z+c)$ or difference
$h(z+c)-h(z)$ or delay-difference $h^{(k)}(z+c)$, here $kgeq 1$ and $c$ is a
non-zero constant. Moreover, we discuss Hayman conjecture for paired complex
differential polynomials when $n=1.$ | | Source: | arXiv, 2208.10818 | | Services: | Forum | Review | PDF | Favorites | |
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