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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 the multiple points of certain meromorphic functions

Author: J. K. Langley
Journal: Proc. Amer. Math. Soc. 123 (1995), 1787-1795
MSC: Primary 30D35
MathSciNet review: 1242092
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Abstract: We show that if f is transcendental and meromorphic in the plane and $ T(r,f) = o{(\log r)^2}$, then f has infinitely many critical values. This is sharp. Further, we apply a result of Eremenko to show that if f is meromorphic of finite lower order in the plane and $ N(r,1/ff'') = o(T(r,f' /f))$, then $ f(z) = \exp (az + b)$ or $ f(z) = {(az + b)^{ - n}}$ with a and b constants and n a positive integer.

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PII: S 0002-9939(1995)1242092-4
Article copyright: © Copyright 1995 American Mathematical Society