## On sharing values of meromorphic functions and their differences.(English)Zbl 1267.30077

The authors obtain a difference analogue of the Brück conjecture and some results on uniqueness. They prove that $$a=0$$ and $\frac{f(z+\eta)-f(z)}{f(z)}=A,$ where $$A$$ is a nonzero constant, if $$f(z)$$ is a finite order transcendental entire function which has a finite Borel exceptional value $$a$$ and $$\Delta f(z)=f(z+\eta)-f(z)\not\equiv 0$$, and if $$\Delta f$$ and $$f$$ share the value $$a$$ CM. Some other results are also obtained. These contributions are interesting and new, and make the Brück conjecture more popular.

### MSC:

 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 39A10 Additive difference equations
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### References:

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