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.

URL: http://projecteuclid.org/euclid.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 α and only finitely many nonreal zeroes, poles and α-points.

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