论文标题
一些差分单元的价值分布
Value distribution of some differential monomials
论文作者
论文摘要
令$ f $为复杂平面$ \ mathbb {c} $中定义的先验杂种功能。我们考虑差分多项式$ f^{q_ {0}}（f^{（k）}）^{q_ {k}} $的值分布，其中$ q_ {0}（\ geq 2），q_ {k {k {k}（k geq 1）$ k（\ geq 1）$ k（\ geq1）$ non-ny-nnegers $ non-nnegersegers。我们以$ \ overline {n} \ left（r，\ frac {1} {f^{q _ {_ {0}}}}}}}}}}}}}}}}}（f^{（k）}}^wermiess ysustry Instrught（r，r，{1}}}）（f^{q _ {0}}）（f^{（k）} {q_________ {等。 （数学不平等应用，14，93-100，2011）和Karmakar and Sahoo（结果数学，73，2018），用于特定类别的先验性异晶功能。
Let $f$ be a transcendental meromorphic function defined in the complex plane $\mathbb{C}$. We consider the value distribution of the differential polynomial $f^{q_{0}}(f^{(k)})^{q_{k}}$, where $q_{0}(\geq 2), q_{k}(\geq 1)$ are $k(\geq1)$ non-negative integers. We obtain a quantitative estimation of the characteristic function $T(r, f)$ in terms of $\overline{N}\left(r,\frac{1}{f^{q_{_{0}}}(f^{(k)})^{q_{k}}-1}\right)$.\par Our result generalizes the results obtained by Xu et al. (Math. Inequal. Appl., 14, 93-100, 2011) and Karmakar and Sahoo (Results Math., 73, 2018) for a particular class of transcendental meromorphic functions.
