论文标题
关于海曼问题的注释
A note on Hayman's problem
论文作者
论文摘要
In this note, it is shown that the differential polynomial of the form $Q(f)^{(k)}-p$ has infinitely many zeros, and particularly $Q(f)^{(k)}$ has infinitely many fixed points for any positive integer $k$, where $f$ is a transcendental meromorphic function, $p$ is a nonzero polynomial and $Q$ is a polynomial with $ f $的小功能领域的系数。结果可以追溯到问题1.19和问题1.20的研究书中的问题1.20。结果，我们对Chiang提出并由Bergweiler审议的零分布的零分布的扩展问题给出了肯定的答案。此外，我们的方法提供了一种统一的方法，可以研究一个具有小的男态系数的一个和几个复杂变量中偏差多项式的零分布的问题。
In this note, it is shown that the differential polynomial of the form $Q(f)^{(k)}-p$ has infinitely many zeros, and particularly $Q(f)^{(k)}$ has infinitely many fixed points for any positive integer $k$, where $f$ is a transcendental meromorphic function, $p$ is a nonzero polynomial and $Q$ is a polynomial with coefficients in the field of small functions of $f$. The results are traced back to Problem 1.19 and Problem 1.20 in the book of research problems by Hayman and Lingham. As a consequence, we give an affirmative answer to an extended problem on the zero distribution of $(f^n)'-p$, proposed by Chiang and considered by Bergweiler. Moreover, our methods provide a unified way to study the problem of the zero distributions of partial differential polynomials of meromorphic functions in one and several complex variables with small meromorphic coefficients.
