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Real meromorphic functions and a result of Hinkkanen and Rossi

Nicks, Daniel (2009). Real meromorphic functions and a result of Hinkkanen and Rossi. Illinois Journal of Mathematics, 53(2) pp. 605–622.

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Abstract

Let f be a transcendental meromorphic function such that all but finitely many of the poles of f and zeroes of f' are real. Generalising a result of Hinkkanen and Rossi (Proc. Amer. Math. Soc. 92 (1984) 72–74), we characterize those f such that f' takes some nonzero value only finitely often, and show that all but finitely many of the zeroes of f'' are real in this case. We also prove a related asymptotic result about real meromorphic functions with a nonzero deficient value α and only finitely many nonreal zeroes, poles and α-points.

Item Type: Journal Article
Copyright Holders: 2010 University of Illinois
ISSN: 0019-2082
Keywords: d.nicks@open.ac.uk
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22688
Depositing User: Daniel Nicks
Date Deposited: 05 Aug 2010 11:57
Last Modified: 27 Oct 2012 15:59
URI: http://oro.open.ac.uk/id/eprint/22688
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