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Meromorphic Functions in the Class S and the Zeros of the Second Derivative

Meromorphic Functions in the Class S and the Zeros of the Second Derivative Let S denote the class of functions f which are transcendental and meromorphic in the plane and have finitely many critical and asymptotic values. It is shown that if f ∈ S has finite lower order and f″/f′ is non-constant then δ(0, f″/f′) = 0. Moreover, the Gol’dberg conjecture holds for a function in S of finite order, at least on a set of logarithmic density 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Meromorphic Functions in the Class S and the Zeros of the Second Derivative

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321671
Publisher site
See Article on Publisher Site

Abstract

Let S denote the class of functions f which are transcendental and meromorphic in the plane and have finitely many critical and asymptotic values. It is shown that if f ∈ S has finite lower order and f″/f′ is non-constant then δ(0, f″/f′) = 0. Moreover, the Gol’dberg conjecture holds for a function in S of finite order, at least on a set of logarithmic density 1.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 27, 2007

References