Differential polynomials and value-sharing

Abstract. In this paper, we give some theorems on uniqueness problem of differential polynomials of meromorphic functions. Let \(a, b\) be non-zero constants and let \(n, m, l, k\) be positive integers satisfying \(n\geq 3l(k+1)+3m+9\) and \(m\geq l(k+1)+1\). If \(f^n+af^m(f^{(k)})^l \;\text{and}\; g^n+ag^m(g^{(k)})^l\) share the value \(b\) CM, then \(f\) and \(g\) are closely related. We also consider the case sharing the value IM.

Key words and phrases. Shared values, differential polynomials, uniqueness of meromorphic functions.