Uniqueness of entire functions sharing an entire function of smaller order with their derivatives
In 1996, \textit{R. Brück} [Result. Math. 30, No. 1--2, 21--24 (1996; Zbl 0861.30032)] conjectured that if \(f\) is a non-constant entire function satisfying \(\sigma_{2}(f) < \infty\), where the hyper-order \(\sigma_{2}(f)\) of \(f\) is not a positive integer, and if \(f\) and \(f'\) share one finite complex number \(a\) CM, then \(f - a = c(f' - a)\) for some constant \(c\neq 0\). This conjecture inspired a lot of researchers to work on the uniqueness problem of an entire function and its derivatives. The present paper also deals with such problems. A number of interesting results are proved in the paper, which involve the sharing of an entire function having slower growth than that of the function sharing it with derivatives.
scientific article; zbMATH DE number 5919508
scientific article