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Uniqueness of difference polynomials
AIMS Mathematics, 2021 Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)
Xiaomei Zhang , Xiang Chen
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Value Sharing Results for q-Shifts Difference Polynomials [PDF]
Discrete Dynamics in Nature and Society, 2013 We investigate the zero distribution of q-shift difference polynomials of meromorphic functions with zero order and obtain some results that extend previous results of K. Liu et al.
Yong Liu +3 more
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On the Deficiencies of Some Differential-Difference Polynomials
Abstract and Applied Analysis, 2014 The characteristic functions of differential-difference polynomials are investigated, and the result can be viewed as a differential-difference analogue of the classic Valiron-Mokhon’ko Theorem in some sense and applied to investigate the deficiencies of
Xiu-Min Zheng, Hong Yan Xu
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Difference inequalities for polynomials in $L_0$
Matematychni Studii, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
É. A. Storozhenko
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Multivariate Difference Gon\v{c}arov Polynomials [PDF]
, 2020 17 ...
Ayomikun Adeniran +2 more
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Value Distributions and Uniqueness of Difference Polynomials
Advances in Difference Equations, 2011 We investigate the zeros distributions of difference polynomials of meromorphic functions, which can be viewed as the Hayman conjecture as introduced by (Hayman 1967) for difference.
TingBin Cao, Xinling Liu, Kai Liu
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Zeros of some difference polynomials [PDF]
Advances in Difference Equations, 2013 In this paper, we study zeros of some difference polynomials in f(z) and their shifts, where f(z) is a finite order meromorphic function having deficient value ∞. These results improve previous findings.
Shuang-ting Lan, Zong-Xuan Chen
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The zeros on complex differential-difference polynomials of certain types
Advances in Difference Equations, 2018 In this paper, we consider the zeros distribution of f(z)P(z,f)−q(z) $f(z)P(z,f) -q(z)$, where P(z,f) $P(z,f)$ is a linear differential-difference polynomial of a finite-order transcendental entire function f(z) $f(z)$, and q(z) $q(z)$ is a nonzero ...
Changjiang Song, Kai Liu, Lei Ma
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Unicity of transcendental meromorphic functions concerning differential-difference polynomials
AIMS Mathematics, 2022 Let $ f $ and $ g $ be two transcendental meromorphic functions of finite order with a Borel exceptional value $ \infty $, let $ \alpha $ $ (\not\equiv 0) $ be a small function of both $ f $ and $ g $, let $ d, k, n, m $ and $ v_j (j = 1, 2, \cdots, d) $
Zhiying He, Jianbin Xiao, Mingliang Fang
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Multivariate Polynomial Values in Difference Sets [PDF]
, 2020 For $\ell\geq 2$ and $h\in \mathbb{Z}[x_1,\dots,x_{\ell}]$ of degree $k\geq 2$, we show that every set $A\subseteq \{1,2,\dots,N\}$ lacking nonzero differences in $h(\mathbb{Z}^{\ell})$ satisfies $|A|\ll_h Ne^{-c(\log N)^ }$, where $c=c(h)>0$, $ =[(k-1)^2+1]^{-1}$ if $\ell=2$, and $ =1/2$ if $\ell\geq 3$, provided $h(\mathbb{Z}^{\ell})$ contains ...
John R. Doyle, Alex Rice
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