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| 摘要: |
| 本文研究了零级的亚纯函数的q-差分多项式的值分布.利用Nevanlinna理论,得到了以下结果.设f是零级的超越亚纯函数,m是非负整数,q,a,c∈C\{0},b∈C,α(z)是f(z)的小函数.如果f(qz+c)-f(z)≢0,n ≥ 5,则f(z)n(f(z)m-a)[f(qz+c)-f(z)]-α(z)和f(z)n+a[f(qz+c)-f(z)]-b有无穷多个零点.该结果改进了定理D中的n ≥ 7和定理E中的n ≥ 8. |
| 关键词: 零级 差分多项式 小函数 Borel例外值 |
| DOI： |
| 分类号:O174.52 |
| 基金项目:Supported by National Natural Science Foundation of China(11371139). |
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| VALUE DISTRIBUTION OF q-SHIFT DIFFERENCEPOLYNOMIALS |
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WANG Qiong-yan,YE Ya-sheng
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| Abstract: |
| In this paper, we investigate the value distribution of q-shift difierence polynomials of meromorphic function with zero order. By using the Nevanlinna theory, we obtain the following result. Let f be a transcendental meromorphic function with zero order, m be a non-negative integer, q,a,c∈C\{0},b∈C,α(z) be a small function of f(z). If f(qz+c)-f(z)≢0, n ≥ 5, then both f(z)n(f(z)m-a) [f(qz + c)-f(z)]-α(z) and f(z)n + a [f(qz + c)-f(z)]-b have inflnitely many zeros, which improve the conditions n ≥ 7 of Theorem D and n ≥ 8 of Theorem E. |
| Key words: zero order difierence polynomial small function Borel exceptional value |
