We say that two meromorphic functions f and g share a small function \(\alpha \) counting multiplicities if \(f-\alpha \) and \(g-\alpha \) admit the same zeros with the same multiplicities. Let Q be a polynomial of one variable. In [Comput. Methods Funct. Theory 17: 613-634, 2017, Theorem. 1.1], we proved that if \((Q(f))^{(k)}\) and \((Q(g))^{(k)}\) share \(\alpha \) counting multiplicities then, with suitable conditions on the degree of Q and on the number of zeros and the multiplicities of the zeros of \(Q'\), there are explicit relations between Q(f) and Q(g). Unfortunately, there is a gap at the beginning of the proof of An and Phuong (Comput. Methods Funct. Theory 17:613–634, 2017, Theorem 1.1]. We will give a way to avoid the gap. This proof can also be used to fix the gaps of other authors’ published papers listed in Schweizer (arXiv:1705.05048v2, 2017).

我们说两个亚纯函数˚F和摹 小函数 \（\阿尔法\） 计数多重如果\（F- \阿尔法\）和\（G- \阿尔法\）承认与同多重相同的零。令Q为一个变量的多项式。在[计算机。方法功能。理论17：613-634，2017，定理。1.1]，我们证明了如果\（（Q（f））^ {（k）} \）和\（（Q（g））^ {（k）} \）共享计算乘数的\（\ alpha \），，在Q度和零个数以及\（Q'\）的零个乘数的合适条件下，在Q（f）和Q（g）之间有明确的关系。不幸的是，在An和Phuong的证明的开头有一个缺口（计算方法函数理论17：613–634，2017，定理1.1]。我们将提供一种避免这种差距的方法。用来弥补Schweizer（arXiv：1705.05048v2，2017）中列出的其他作者发表的论文之间的差距。