On value distribution of f (k)-af n

The aim of this paper is to discuss the value distribution of the function f ^(k) − af ⁿ. Under the assumption that f(z) is a transcendental meromorphic function in the complex plane and a is a non-zero constant, it is proved that if n ⩽ k + 3, then f ^(k) − af ⁿ has infinitely many zeros. The main result is obtained by using the Nevanlinna theory and the Clunie lemma of complex functions. __________ Translated from Acta Scientiarum Naturalium Universitatis NeiMongol, 2004, 35(1): 5–9