A note on Hayman's conjecture
Complex Variables
2020-03-20 v1
Abstract
In this paper, we will give suitable conditions on differential polynomials such that they take every finite non-zero value infinitely often, where 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 \cite{HL}. As consequences, we give a new proof of the Hayman conjecture. Moreover, our results allow differential polynomials to have some terms of any degree of and also the hypothesis in \cite[Theorem 2]{BE} is replaced by in our result.
Cite
@article{arxiv.2003.08846,
title = {A note on Hayman's conjecture},
author = {Ta Thi Hoai An and Nguyen Viet Phuong},
journal= {arXiv preprint arXiv:2003.08846},
year = {2020}
}