Quantum ergodicity of Eisenstein series for Bianchi groups

Abstract

We prove the quantum ergodicity of Eisenstein series on the arithmetic hyperbolic 3-manifold ${\mathrm{PSL}}_2({\mathcal{O}}_F)\backslash {\mathbb{H}}^3$, where $F$ is an imaginary quadratic field with ring of integers ${\mathcal{O}}_F$ and class number $h_F\ge 1$. 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.

arXiv comment23 pages