The main purpose of this article is concerned with the uniqueness of meromorphic functions in the $k$-punctured complex plane $\Omega$ sharing five small functions with finite weights. We proved that for any two admissible meromorphic functions $f$ and $g$ in $\Omega$, if $\widetilde{E}_\Omega(\alpha_j,l;f)=\widetilde{E}_\Omega(\alpha_j,l; g)$ and an integer $l\geq 22$, then $f\equiv g$, where $\alpha_j~(j=1,2,\ldots,5)$ are five distinct small functions with respect to $f$ and $g$. Our results are extension and improvement of previous theorems given by Ge and Wu, Cao and Yi.

中文翻译：

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亚纯函数在k点复平面上共享小函数的唯一性

本文的主要目的涉及在$ k $穿孔的复平面$ \ Omega $中亚纯函数的唯一性，它们共享五个具有有限权重的小函数。我们证明了对于$ \ Omega $中的任何两个亚纯函数$ f $和$ g $，如果$ \ widetilde {E} _ \ Omega（\ alpha_j，l; f）= \ widetilde {E} _ \ Omega（ \ alpha_j，l; g）$和一个整数$ l \ geq 22 $，然后是$ f \ equiv g $，其中$ \ alpha_j〜（j = 1,2，\ ldots，5）$是五个不同的小函数，关于$ f $和$ g $。我们的结果是对Ge和Wu，Cao和Yi给出的先前定理的扩展和改进。