On the rate of equidistribution of expanding horospheres in finite-volume quotients of $\mathrm{S}\mathrm{L}(2,\mathbb{C})$

Let $\mathrm{\Gamma }$ be a lattice in $G=\mathrm{S}\mathrm{L}(2,\mathbb{C})$. We give an effective equidistribution result with precise error terms for expanding translates of pieces of horospherical orbits in $\mathrm{\Gamma }\mathrm{\backslash }G$. Our method of proof relies on the theory of unitary representations.