Recently, various results on the existence of deficient value or infinitely many zeros of several special classes of differential polynomials of an entire function or a transcendental meromorphic function f satisfying...Recently, various results on the existence of deficient value or infinitely many zeros of several special classes of differential polynomials of an entire function or a transcendental meromorphic function f satisfying δ(∞, f)=1 have been obtained. In this paper, we have summarized some of them and extended these results by obtaining some quantitative estimations on the zeros of several general classes of differential polynomials of an arbitrary transcendental meromorphic function. The proofs utilize the improved version of the Clunie lemma on differential polynomials and carefully count the multiplicities of the zeros of various auxiliary functions.展开更多
基金Project partially supported by U. P. G. C., Hong Kong and partially supported by the National Natural Science Foundation of China.
文摘Recently, various results on the existence of deficient value or infinitely many zeros of several special classes of differential polynomials of an entire function or a transcendental meromorphic function f satisfying δ(∞, f)=1 have been obtained. In this paper, we have summarized some of them and extended these results by obtaining some quantitative estimations on the zeros of several general classes of differential polynomials of an arbitrary transcendental meromorphic function. The proofs utilize the improved version of the Clunie lemma on differential polynomials and carefully count the multiplicities of the zeros of various auxiliary functions.
