Let $f:X\rightarrow Y$ be a finite morphism (a branched covering) of degree $n$ of smooth complex algebraic curves.
It is a known result that for any line bundle $L$ on $X$, the pushforward $f_* L$ is a vector bundle of rank $n$ (i.e. the pushforward sheaf of the sheaf of sections of $L$ is locally free and of rank $n$).
Could anyone give a reference for a simple proof of this result? I know it can be derived as a particular case of more general results, but I am interested in this simple case.