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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Zeros of the successive derivatives of Hadamard gap series


Author: Robert M. Gethner
Journal: Trans. Amer. Math. Soc. 339 (1993), 799-807
MSC: Primary 30D35; Secondary 30B10
MathSciNet review: 1123453
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Abstract: A complex number $ z$ is in the final set of an analytic function $ f$, as defined by Pólya, if every neighborhood of $ z$ contains zeros of infinitely many $ {f^{(n)}}$. If $ f$ is a Hadamard gap series, then the part of the final set in the open disk of convergence is the origin along with a union of concentric circles.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1123453-3
Keywords: Final set, successive derivatives, Hadamard gaps, gap series
Article copyright: © Copyright 1993 American Mathematical Society