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Entire functions that share a small function with their derivatives. (English) Zbl 1069.30049

The paper deals with the uniqueness problem of an entire function that shares a small function with its derivatives. The authors prove two main results, one of which may be stated as follows: Let \(f\) be a nonconstant entire function and \(a = a(z) (\not\equiv 0)\) be a small function related to \(f\). If \(f\), \(f^{(k)}\) and \(f^{(1+k)}\) share \(a\) CM then \(f \equiv f'\), where \(k\) is a positive integer.
Though the statements of the theorems are simple, the proofs are much involved and sophisticated.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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