A unicity theorem for entire functions concerning differential polynomials.(English)Zbl 1005.30023

Summary: We study the value distribution of entire functions and prove the following theorem: Let $$f(z)$$ and $$g(z)$$ be two transcendental entire functions, $$n\geq 11$$ be a positive integer. If $$f^n(z)(f(z)- 1)f'(z)$$ and $$g^n(z)(g(z)- 1)g'(z)$$ share 1 CM, then $$f(z)\equiv g(z)$$.

MSC:

 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D20 Entire functions of one complex variable (general theory)