Order of a zero of a differential
= Order of a zero of a differential
{title2=$\operatorname{ord}_p(q)=m$}
= Zero order
{synonym}
If a local <holomorphic> $r$-differential is $z^m u(z)\,dz^r$, where $u(0)\ne0$, its <zero order> is $m$. The order is unchanged by a <holomorphic> coordinate change with nonzero <derivative>. For a <holomorphic one-form> the <cone angle> is $2\pi(m+1)$, and for a <holomorphic quadratic differential> it is $(m+2)\pi$.