## 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.

### MSC:

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

### Keywords:

order of growth; shared value
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