On the multiple points of certain meromorphic functions

Langley, J. K.

doi:10.1090/S0002-9939-1995-1242092-4

On the multiple points of certain meromorphic functions

Author: J. K. Langley
Journal: Proc. Amer. Math. Soc. 123 (1995), 1787-1795
MSC: Primary 30D35
DOI: https://doi.org/10.1090/S0002-9939-1995-1242092-4
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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