Derivatives of meromorphic functions and sine function

作者:Yang, Pai*; Liu, Xiaojun; Pang, Xuecheng
来源:Proceedings of the Japan Academy Series A-Mathematical Sciences, 2015, 91(9): 129-134.
DOI:10.3792/pjaa.91.129

摘要

In the paper, we take up a new method to prove the following result. Let f be a meromorphic function in the complex plane, all of whose zeros have multiplicity at least k + 1 (k >= 2) and all of whose poles are multiple. If T(r, sin z) = o{T(r, f(z))} as n -> infinity, then f((k))(z) - sin z has infinitely many zeros.