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

On Picard's theorem for entire quasiregular mappings


Author: Matti Vuorinen
Journal: Proc. Amer. Math. Soc. 107 (1989), 383-394
MSC: Primary 30C60; Secondary 30D40
MathSciNet review: 975662
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Abstract: Several refinements of Picard's theorem for entire functions in the complex plane have been proved by many authors in connection with the theory of Picard sets. We prove a result of this type for entire quasiregular mappings in euclidean $ n$-space in the case when the "Picard set" consists of a sequence $ {a_k}$ on a ray emanating from 0 with $ \vert{a_k}\vert = {2^k}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0975662-6
PII: S 0002-9939(1989)0975662-6
Article copyright: © Copyright 1989 American Mathematical Society