On uniqueness of an entire function and its derivatives. (English) Zbl 1131.30013

Authors’ summary: We study the growth of solutions of a first order linear differential equation. From this we verify that a conjecture given by Brük is true under the restriction of the hyper order less than \(1/2\), and obtain some uniqueness theorems of a nonconstant entire function and its first derivative sharing a nonzero constant CM. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible.


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D30 Meromorphic functions of one complex variable (general theory)
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