On a problem of Hellerstein, Shen and Williamson
HTML articles powered by AMS MathViewer
- by A. Hinkkanen and J. Rossi PDF
- Proc. Amer. Math. Soc. 92 (1984), 72-74 Request permission
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 $C$.References
- Steven B. Bank and Ilpo Laine, On the oscillation theory of $f^{\prime \prime }+Af=0$ where $A$ is entire, Trans. Amer. Math. Soc. 273 (1982), no. 1, 351–363. MR 664047, DOI 10.1090/S0002-9947-1982-0664047-6
- Albert Edrei, Meromorphic functions with three radially distributed values, Trans. Amer. Math. Soc. 78 (1955), 276–293. MR 67982, DOI 10.1090/S0002-9947-1955-0067982-9
- Simon Hellerstein and Jack Williamson, Derivatives of entire functions and a question of Pólya, Trans. Amer. Math. Soc. 227 (1977), 227–249. MR 435393, DOI 10.1090/S0002-9947-1977-0435393-4
- Simon Hellerstein, Li Chien Shen, and Jack Williamson, Reality of the zeros of an entire function and its derivatives, Trans. Amer. Math. Soc. 275 (1983), no. 1, 319–331. MR 678353, DOI 10.1090/S0002-9947-1983-0678353-3 —, Abstracts Amer. Math. Soc. 4 (1983), 252.
- George Pólya, Collected papers, Mathematicians of Our Time, Vol. 7, MIT Press, Cambridge, Mass.-London, 1974. Vol. 1: Singularities of analytic functions; Edited by R. P. Boas. MR 0505093
- Hans Wittich, Neuere Untersuchungen über eindeutige analytische Funktionen, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 8, Springer-Verlag, Berlin-New York, 1968 (German). Zweite, korrigierte Auflage. MR 0244490
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 72-74
- MSC: Primary 30D35
- DOI: https://doi.org/10.1090/S0002-9939-1984-0749894-1
- MathSciNet review: 749894