2020/03/19 by Ta Thi Hoai An, An, Ta Thi Hoai, Nguyen Viet Phuong +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV
paper · pdf · doi:10.48550/arxiv.2003.08846
arxiv created 2020/03/19 · arxiv updated 2020/03/20
In this paper, we will give suitable conditions on differential polynomials Q(f) such that they take every finite non-zero value infinitely often, where f is a meromorphic function in complex plane. These results are related to Problem 1.19 and Problem 1.20 in a book of Hayman and Lingham \citeHL. As consequences, we give a new proof of the Hayman conjecture. Moreover, our results allow differential polynomials Q(f) to have some terms of any degree of f and also the hypothesis n>k in \cite[Theorem 2]BE is replaced by n≥ 2 in our result.