Let $X$ be a compact Riemann surface, and $f$ a meromorphic function on X. There's a theorem telling us that $\deg(\mathrm{div}(f)) = 0$.
But is also true the inverse statement? I mean is it true that:
if $D$ is a divisor on $X$ with $\deg(D) = 0$, then exists a meromorphic function $f$ on $X$ such that $D = \mathrm{div}(f)$?
Thanks!