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 \(f(z)\equiv g(z)\).


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