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1983•Transactions of the American Mathematical SocietyRequires access

Reality of the Zeros of An Entire Function and Its Derivatives

Simon Hellerstein, LI-Chen Shen, Jack Williamson

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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.

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What this paper is about

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.

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OpenAlex reports 10 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Entire function, Mathematics, Function (biology), Pure mathematics, Real-valued function, Algebra over a field, Discrete mathematics, Evolutionary biology

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