Reality of the zeros of an entire function and its derivatives-Reference-Cited by-同舟云学术

Reality of the zeros of an entire function and its derivatives

Published:1983 Issue:1 Volume:275 Page:319-331
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Hellerstein Simon,Shen Li Chien,Williamson Jack

Abstract

In 1914 Pólya raised the problem of classifying the entire functions which together with all their derivatives have only real zeros. In earlier work Hellerstein and Williamson settled this problem for entire functions which are real on the real axis. We complete the classification in all cases and show that it is sufficient to consider the function and its first two derivatives.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1983-275-01/S0002-9947-1983-0678353-3/S0002-9947-1983-0678353-3.pdf

Reference16 articles.

1. M. Ålander, Sur les fonctions entières qui ont tous leurs zéros sur une droit, C. R. Acad. Sci. Paris Sér. A-B 176 (1923), 158-161.

2. Meromorphic functions with three radially distributed values;Edrei, Albert;Trans. Amer. Math. Soc.,1955

3. Picard values of meromorphic functions and their derivatives;Hayman, W. K.;Ann. of Math. (2),1959

4. On the zeros of an entire function and its second derivative;Hellerstein, Simon;Illinois J. Math.,1966

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