论文标题
关于海曼猜想的笔记
A note on Hayman's conjecture
论文作者
论文摘要
在本文中，我们将在差异多项式$ q（f）$上提供适当的条件，以便它们将每个有限的非零值无限地占据，其中$ f $是复杂平面中的meromormorthic函数。这些结果与Hayman和Lingham \ Cite {HL}的书1.19和问题1.20有关。结果，我们给出了海曼猜想的新证明。此外，我们的结果允许差异多项式$ q（f）$具有任何程度的$ f $，以及假设$ n> k $ in \ cite [theorem 2] {be}在我们的结果中被$ n \ ge 2 $取代。
In this paper, we will give suitable conditions on differential polynomials $Q(f)$ such that they take every finite non-zero value infinitely often, where $f$ is a meromorphic function in complex plane. These results are related to Problem 1.19 and Problem 1.20 in a book of Hayman and Lingham \cite{HL}. As consequences, we give a new proof of the Hayman conjecture. Moreover, our results allow differential polynomials $Q(f)$ to have some terms of any degree of $f$ and also the hypothesis $n>k$ in \cite[Theorem 2]{BE} is replaced by $n\ge 2$ in our result.
