# Orbifold matlab problem

1. Mar 1, 2013

### rbwang1225

$\mathbb Z_{\frac{m}n}$ orbifold

1. The problem statement, all variables and given/known data
Consider the identification $z\sim ze^{2\pi i \frac{m}n}$, where $m$ and $n$ are relatively prime integers. Determine a fundamental domain for the identification.

2. Relevant equations
Given two relatively prime integers $a$ and $b$, there exist integers $m$ and $n$ s.t. $ma+nb=1$.

3. The attempt at a solution
By considering cases of small $m,n$'s, I conclude that the fundamental domain is $0\le arg(z)<gcd(\frac{2m}n,2)$, but I can't give a more rigorous proof.
I guess that needs some knowledge of basic number theory.
Any advices would be very appreciated.

Regards.