Drasin's problems and Mues' conjecture
type: Item
instance of: scholarly article
title: Drasin's problems and Mues' conjecture
zbMATH Open document ID: 0760.30011
author: Lo Yang
author: Yaofei Wang
published in: Science in China. Series A
publication date: 1993-04-01T00:00:00Z
review text: Several results concerning the deficiencies of meromorphic functions are obtained. Denote, as usual, the deficiency of \(f\) at \(a\) by \(\delta(a,f)\). It is proved that if \(k\geq 1\), then \[ \sum_{a\in C} \delta(a,f)+\sum_{b\in C} \delta(b,f^{(k)})\leq 3. \] This answers a question of D. Drasin. The inequality is sharp and further results are given in the case of equality. Another result obtained in this paper is that there exists a constant \(K(f)\) such that if \(k\geq K(f)\), then \[ \sum_{a\in C} \delta(a,f^{(k)})\leq 1.\tag{1} \] This is a partial solution to a conjecture of E. Mues which says that (1) holds for all \(k\geq 1\). In a forthcoming paper, the second author has improved on the latter result by showing that there are at most four values of \(k\) for which (1) can fail.
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 148452
zbMATH Keywords: Mues conjecture
zbMATH Keywords: deficiencies
zbMATH Keywords: meromorphic functions
reviewed by: Walter Bergweiler
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 148452