We prove the quantum ergodicity of Eisenstein series on the arithmetic hyperbolic 3-manifold $\operatorname{ PSL}_2(\mathcal{ O}_F)\backslash \mathbb{ H}^3$, where $F$ is an imaginary quadratic field with ring of integers $\mathcal{ O}_F$ and class number $h_F\geq 1$. This extends the work of Koyama, who proved the result in the case $h_F=1$, and establishes the first instance of quantum ergodicity of Eisenstein series over number fields with nontrivial class groups.
Categories: math.NT