Entire functions sharing one polynomial with their derivatives

In this paper, we study the growth of solutions of a k -th order linear differential equation and that of a k + 1-th order linear differential equation. From this we affirmatively answer a uniqueness question concerning a conjecture given by Brück in 1996 under the restriction of the hyper order les...

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Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2008-02, Vol.118 (1), p.13-26
Main Authors: Li, Xiao-Min, Gao, Cun-Chen
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this paper, we study the growth of solutions of a k -th order linear differential equation and that of a k + 1-th order linear differential equation. From this we affirmatively answer a uniqueness question concerning a conjecture given by Brück in 1996 under the restriction of the hyper order less than 1/2, and obtain some uniqueness theorems of a nonconstant entire function and its derivative sharing a finite nonzero complex number CM. The results in this paper also improve some known results. Some examples are provided to show that the results in this paper are best possible.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-008-0002-z