part-ii/2011-132/

[tripos-comments[bot]]

Part II 2011 Riemann Surfaces: Paper 3, Section II, G

https://questions.tripos.org/part-ii/2011-132/

[eha1234]

For the last part, there are n+1 potential branch points at the nth roots of unity and infinity. I considered the monodromy group. The loops around the nth roots of unity cycle the r roots of unity in the same way, so correspond to the same r cycle. The loop around infinity is the composition of these, and splits into n 1 cycles (i.e. is the identity) iff r divides n.