On certain type of difference polynomials of meromorphic functions

Ranran Zhang; Zhibo Huang

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arXiv · 1710.01521

On certain type of difference polynomials of meromorphic functions

Ranran Zhang·Zhibo Huang

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Abstract

In this paper, we investigate zeros of difference polynomials of the form $f(z)^nH(z, f)-s(z)$, where $f(z)$ is a meromorphic function, $H(z, f)$ is a difference polynomial of $f(z)$ and $s(z)$ is a small function. We first obtain some inequalities for the relationship of the zero counting function of $f(z)^nH(z, f)-s(z)$ and the characteristic function and pole counting function of $f(z)$. Based on these inequalities, we establish some difference analogues of a classical result of Hayman for meromorphic functions. Some special cases are also investigated. These results improve previous findings.

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Ranran Zhang, Zhibo Huang. 2017-10-04. On certain type of difference polynomials of meromorphic functions. https://arxiv.org/abs/1710.01521

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