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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The order of entire functions with radially distributed zeros


Author: Faruk F. Abi-Khuzam
Journal: Proc. Amer. Math. Soc. 82 (1981), 71-75
MSC: Primary 30D20; Secondary 30D35
MathSciNet review: 603604
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Abstract: It is shown that an entire function with radially distributed zeros has finite order $ \lambda $ if it has finite lower order $ \mu $. It is then shown that functions with real negative zeros only are extremal for the problem of maximizing the Nevanlinna characteristic in the class of entire functions satisfying $ \lambda - \mu > 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0603604-4
Keywords: Order, lower order of an entire function
Article copyright: © Copyright 1981 American Mathematical Society