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Date: 10-6-2021
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Date: 25-6-2017
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Date: 4-7-2017
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For a point , with
, the ramification index of
at
is a positive integer
such that there is some open neighborhood
of
so that
has only one preimage in
, i.e.,
, and for all other points
,
. In other words, the map from
to
is
to 1 except at
. At all but finitely many points of
, we have
. Note that for any point
we have
. Sometimes the ramification index of
at
is called the valency of
.
REFERENCES:
Jones, G. A. and Singerman, D. Complex Functions Cambridge, England: Cambridge University Press, p. 196, 1987.
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