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Proceedings of the American Mathematical Society

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On a problem of Hellerstein, Shen and Williamson


Authors: A. Hinkkanen and J. Rossi
Journal: Proc. Amer. Math. Soc. 92 (1984), 72-74
MSC: Primary 30D35
MathSciNet review: 749894
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Abstract: Suppose that $ f$ is a nonentire transcendental meromorphic function, real on the real axis, such that $ f$ and $ f'$ have only real zeros and poles, and $ f'$ omits a nonzero value. Confirming a conjecture of Hellerstein, Shen and Williamson, it is shown that then $ f$ is essentially $ f\left( z \right) = \tan z - Bz - C$ for suitable values of $ B$ and $ C$.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0749894-1
Article copyright: © Copyright 1984 American Mathematical Society