Uniqueness theorems on entire functions and their derivatives (Q5927553)

The main result of this paper is the following theorem 1. Let \(f(z)\) be an entire function, let \(a\) be a finite nonzero value, and let \(n\) be a positive integer. If \(f\), \(f^{(n)}\) and \(f^{(n+1)}\) such that \(f-a\), \(f^{(n)}-a\) and \(f^{(n+1)}-a\) have the same zeros counting multiplicities, then \(f=f'\). This theorem gives the answer to the problem of L. Z. Yang.