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Transactions of the American Mathematical Society

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



Further results on prime entire functions

Authors: Fred Gross and Chung Chun Yang
Journal: Trans. Amer. Math. Soc. 192 (1974), 347-355
MSC: Primary 30A20
MathSciNet review: 0349972
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Abstract: Let H denote the set of all the entire functions $ f(z)$ of the form: $ f(z) \equiv h(z){e^{p(z)}} + k(z)$ where $ p(z)$ is a nonconstant polynomial of degree m, and $ h(\nequiv\;0)$, $ k(\nequiv$ constant) are two entire functions of order less than m. In this paper, a necessary and sufficient condition for a function in H to be a prime is established. Several generalizations of known results follow. Some sufficient conditions for primeness of various subclasses of H are derived. The methods used in the proofs are based on Nevanlinna's theory of meromorphic functions and some elementary facts about algebraic functions.

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Keywords: Factorization, factor, entire function, meromorphic function, prime function, pseudo-prime function, R-polynomial prime, Nevanlinna theory, E-prime
Article copyright: © Copyright 1974 American Mathematical Society

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