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Summer 2009 Real meromorphic functions and a result of Hinkkanen and Rossi
Daniel A. Nicks
Illinois J. Math. 53(2): 605-622 (Summer 2009). DOI: 10.1215/ijm/1266934796

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 $\alpha$ and only finitely many nonreal zeroes, poles and $\alpha$-points.

Citation

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Daniel A. Nicks. "Real meromorphic functions and a result of Hinkkanen and Rossi." Illinois J. Math. 53 (2) 605 - 622, Summer 2009. https://doi.org/10.1215/ijm/1266934796

Information

Published: Summer 2009
First available in Project Euclid: 23 February 2010

zbMATH: 1195.30052
MathSciNet: MR2594647
Digital Object Identifier: 10.1215/ijm/1266934796

Subjects:
Primary: 30D35

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

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Vol.53 • No. 2 • Summer 2009
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