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*

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## References

Jones, G. A. and Singerman, D.*Complex Functions*Cambridge, England: Cambridge University Press, p. 196, 1987.

## Referenced on Wolfram|Alpha

Ramification 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