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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A proof of the Pólya-Wiman conjecture


Author: Young-One Kim
Journal: Proc. Amer. Math. Soc. 109 (1990), 1045-1052
MSC: Primary 30D20; Secondary 30D35
MathSciNet review: 1013971
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f(z) = {e^{ - \alpha {z^2}}}g(z)$ where $ \alpha \geq 0$ and $ g$ is a real entire function of genus at most 1. It is shown that if $ f$ has only a finite number of nonreal zeros, then its derivatives, from a certain one onward, have only real zeros.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1013971-3
PII: S 0002-9939(1990)1013971-3
Keywords: Pólya-Wiman conjecture, Laguerre-Pólya class
Article copyright: © Copyright 1990 American Mathematical Society



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