Nonvanishing of ray class $L$-functions

We study the nonvanishing of central values of ray class $L$-functions over a fixed imaginary quadratic field $K$. We prove that, as $\mathrm{N}(\mathfrak{f})$ tends to infinity, at least a proportion $1\mathrm{/}3-{\mathsf{o}}_K(1)$ of the primitive ray class characters $\chi$ modulo $\mathfrak{f}$ satisfy $L(1\mathrm{/}2,\chi )\mathrm{\ne }0$. Our proof adapts the classical mollifier method to the ray class setting and establishes asymptotic formulas for the first and second mollified moments.