Paired Hayman conjecture and uniqueness of complex delay-differential polynomials
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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.
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 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.
참고문헌 (22)
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