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 
.
Ramification Index
This entry contributed by Helena Verrill
Explore with Wolfram|Alpha
References
Jones, G. A. and Singerman, D. Complex Functions Cambridge, England: Cambridge University Press, p. 196, 1987.Referenced on Wolfram|Alpha
Ramification IndexCite this as:
Verrill, Helena. "Ramification Index." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/RamificationIndex.html