Quantum ergodicity of Eisenstein series for Bianchi groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918393811042304 |
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| author | Kim, Doyon Lee, Youngmin |
| author_facet | Kim, Doyon Lee, Youngmin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16518 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum ergodicity of Eisenstein series for Bianchi groups Kim, Doyon Lee, Youngmin Number Theory 11F41, 11M36, 58J51 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. |
| title | Quantum ergodicity of Eisenstein series for Bianchi groups |
| topic | Number Theory 11F41, 11M36, 58J51 |
| url | https://arxiv.org/abs/2603.16518 |