In this paper we estimate the size of the ρn’s in the famous L. Zalcman’s Lemma. With it, we obtain a uniqueness theorem for entire functions and their first derivatives, which improves and generalizes the related results of Rubel and Yang and of Li and Yi. Some examples are provided to show the sharpness of our result. As an application, we prove that R. Brück’s conjecture is true for a class of functions.
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机译：在本文中，我们估计了著名的L. Zalcman的引理中ρ n 的大小。有了它，我们获得了整个函数及其一阶导数的唯一性定理，从而改善并推广了Rubel和Yang以及Li和Yi的相关结果。提供了一些示例以显示我们的结果的清晰度。作为应用，我们证明了R.Brück的猜想对于一类函数是正确的。
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