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Proceedings of the American Mathematical Society

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On a problem of Erdős concerning the zeros of the derivatives of an entire function


Authors: K. F. Barth and W. J. Schneider
Journal: Proc. Amer. Math. Soc. 32 (1972), 229-232
MSC: Primary 30A66
DOI: https://doi.org/10.1090/S0002-9939-1972-0293089-7
MathSciNet review: 0293089
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Abstract: Let $ \{ {S_k}\} $ be any sequence of sets in the complex plane, each of which has no finite limit point. The authors prove, answering affirmatively a question posed by P. Erdös, that there exists a sequence $ \{ {n_k}\} $ of positive integers and a transcendental entire function $ f(z)$ such that $ {f^{({n_k})}}(z) = 0$ if $ z \in {S_k}$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293089-7
Keywords: Derivatives of an entire function, interpolation in the complex plane
Article copyright: © Copyright 1972 American Mathematical Society

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