Some Note on Exceptional Values of Meromorphic Functions
1963 ◽
Vol 22
◽
pp. 189-201
◽
Keyword(s):
A Value
◽
LetEbe a totally-disconnected compact set in thez-plane and letΩbe its complement with respect to the extendedz-plane. ThenΩis a domain and we can consider a single-valued meromorphic functionw = f(z)onΩwhich has a transcendental singularity at each point ofE. Suppose thatEis a null-set of the classWin the sense of Kametani [4] (the classNBin the sense of Ahlfors and Beurling [1]). Then the cluster set off(z)at each transcendental singularity is the wholew-plane, and hencef(z)has an essential singularity at each point ofE. We shall say that a valuewis exceptional forf(z)at an essential singularity ζ ∈Eif there exists a neighborhood of ζ where the functionf(z)does not take this valuew.
1961 ◽
Vol 18
◽
pp. 171-191
◽
Keyword(s):
1966 ◽
Vol 27
(1)
◽
pp. 213-222
◽
1982 ◽
Vol 88
◽
pp. 133-154
◽
Keyword(s):
2002 ◽
Vol 132
(3)
◽
pp. 531-544
◽
Keyword(s):
1968 ◽
Vol 32
◽
pp. 277-282
◽