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