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Transactions of the American Mathematical Society

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



On the functional equation $ f\sp{2}=e\sp{2\phi\sb{1}}+e\sp{2\phi\sb{2}}+e\sp{2\phi\sb{3}}\ $ and a new Picard theorem

Author: Mark Green
Journal: Trans. Amer. Math. Soc. 195 (1974), 223-230
MSC: Primary 30A70; Secondary 30A20
MathSciNet review: 0348112
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Abstract: By analogy with E. Borel's reduction of the classical Picard theorem to an analytic statement about linear relations among exponentials of entire functions, a new Picard theorem is proved by considering the functional relation $ {f^2} = {e^{2{\phi _1}}} + {e^{2{\phi _2}}} + {e^{2{\phi _3}}}$ for entire functions. The analytic techniques used are those of Nevanlinna theory.

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Keywords: Picard theorem, value distribution theory, exponential function, Nevanlinna theory, quadric, entire function
Article copyright: © Copyright 1974 American Mathematical Society

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