Meromorphic functions in the class \(S\) and the zeros of the second derivative
type: Item
instance of: scholarly article
title: Meromorphic functions in the class \(S\) and the zeros of the second derivative
zbMATH Open document ID: 1151.30023
DOI: 10.1007/BF03321671
published in: Computational Methods and Function Theory
publication date: 2008-07-29T00:00:00Z
full work available at URL: cmf08007.htm
review text: Let \(S\) be a class of transcendental meromorphic functions in the plane that have finitely many critical and asymptotic values. The author has proved that if \(f \in S\) has finite order (respectively finite lower order), \(f''/f'\) is non-constant and \(f^{-1}\) has finitely many singular values. Then \[ \log^+ M(r, f''/f') = o (T(r, f''/f')) \] as \(r \to \infty\) in a set of logarithmic density 1 (respectively upper logarithmic density 1). Here \(M\) and \(T\) are the standard notions of the Nevanlina theory (Theorem 4). Moreover in these conditions the Nevanlinna deficiency \(\delta (0, f''/f') = 0\) (Theorem 5).
reviewed by: P. Z. Agranovich
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 5305521
zbMATH Keywords: Nevanlinna deficiency
zbMATH Keywords: singularity
zbMATH Keywords: inverse function
author: James K. Langley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5305521