Entire functions sharing polynomials with their first derivatives |
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| Authors: | Feng Lü Junfeng Xu Ang Chen |
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| Institution: | (1) Department of Mathematics, China University of Petroleum, Dongying, Shandong, 257061, P.R. China;(2) Department of Mathematics, Wuyi University, Jiangmen, Guangdong, 529020, P.R. China;(3) Department of Mathematics, Shandong University, Jinan, Shandong, 250100, P.R. China |
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| Abstract: | 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.
Received: 30 October 2008, Revised: 5 February 2009 |
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| Keywords: | " target="_blank"> Entire functions Nevanlinna theory uniqueness normal family |
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