## Illinois Journal of Mathematics

### Real meromorphic functions and a result of Hinkkanen and Rossi

Daniel A. Nicks

#### 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.

#### Article information

Source
Illinois J. Math., Volume 53, Number 2 (2009), 605-622.

Dates
First available in Project Euclid: 23 February 2010

https://projecteuclid.org/euclid.ijm/1266934796

Digital Object Identifier
doi:10.1215/ijm/1266934796

Mathematical Reviews number (MathSciNet)
MR2594647

Zentralblatt MATH identifier
1195.30052

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory

#### Citation

Nicks, Daniel A. Real meromorphic functions and a result of Hinkkanen and Rossi. Illinois J. Math. 53 (2009), no. 2, 605--622. doi:10.1215/ijm/1266934796. https://projecteuclid.org/euclid.ijm/1266934796

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