Reality of the zeros of an entire function and its derivatives
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- by Simon Hellerstein, Li Chien Shen and Jack Williamson PDF
- Trans. Amer. Math. Soc. 275 (1983), 319-331 Request permission
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.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 275 (1983), 319-331
- MSC: Primary 30D20; Secondary 30D30, 30D35
- DOI: https://doi.org/10.1090/S0002-9947-1983-0678353-3
- MathSciNet review: 678353