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arXiv · 2603.16518

Quantum ergodicity of Eisenstein series for Bianchi groups

Doyon Kim·Youngmin Lee
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Abstract

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.

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Doyon Kim, Youngmin Lee. 2026-03-17. Quantum ergodicity of Eisenstein series for Bianchi groups. https://arxiv.org/abs/2603.16518

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