An application of counting ideals in ray classes

We prove a fully explicit generalized Brun–Titchmarsh theorem for an imaginary quadratic field $\mathbf K$. More precisely, for any finite family of linearly independent linear forms with coefficients in $\mathcal O_{\mathbf K}$, we count the number of integers at which all these linear forms take prime values in $\mathcal O_{\mathbf K}$.