Let $X$ be a complex manifold, let $\mathcal{M}(X)^*$ denote the multiplicative group of meromorphic functions on $X$ that are not identically zero on any connected component of $X$, and let $\operatorname{Div}(X)$ denote the abelian group of divisors on $X$. For $f \in \mathcal{M}(X)^*$, write