Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.

We prove that any divisor $Y$ of a global analytic set $X\subset {ℝ}^n$ has a generic equation, that is, there is an analytic function vanishing on $Y$ with multiplicity one along each irreducible component of $Y$. We also prove that there are functions with arbitrary multiplicities along $Y$. The main result states that if $X$ is pure dimensional, $Y$ is locally principal, $X/Y$ is not connected and $Y$ represents the zero class in $H_{q-1}^{\infty }(X,{\mathbb{Z}}_2)$ then the divisor $Y$ is globally principal.