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Entire functions with almost radially distributed values


Author: Shigeru Kimura
Journal: Proc. Amer. Math. Soc. 71 (1978), 73-78
MSC: Primary 30A70
DOI: https://doi.org/10.1090/S0002-9939-1978-0486525-X
MathSciNet review: 0486525
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Abstract: Let $ f(z)$ be an entire function of finite lower order. Assume that there exist a positive number h and an unbounded sequence $ \{ {w_n}\} _{n = 1}^\infty $ such that all roots of the equations $ f(z) = {w_n}(n = 1,2, \ldots )$ lie in $ \{ z;\vert\operatorname{Im} z\vert < h\} $. Then $ f(z)$ is a polynomial of degree not greater than two. The hypothesis of the finiteness of lower order of $ f(z)$ cannot be removed.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0486525-X
Keywords: Entire function, almost radially distributed value, lower order, deficiency
Article copyright: © Copyright 1978 American Mathematical Society

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