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Quantum ergodicity of Eisenstein series for Bianchi groups

Number Theory 2026-03-18 v1

Abstract

We prove the quantum ergodicity of Eisenstein series on the arithmetic hyperbolic 3-manifold PSL2(OF)\H3\operatorname{PSL}_2(\mathcal{O}_F)\backslash \mathbb{H}^3, where FF is an imaginary quadratic field with ring of integers OF\mathcal{O}_F and class number hF1h_F\geq 1. This extends the work of Koyama, who proved the result in the case hF=1h_F=1, and establishes the first instance of quantum ergodicity of Eisenstein series over number fields with nontrivial class groups.

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Cite

@article{arxiv.2603.16518,
  title  = {Quantum ergodicity of Eisenstein series for Bianchi groups},
  author = {Doyon Kim and Youngmin Lee},
  journal= {arXiv preprint arXiv:2603.16518},
  year   = {2026}
}

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23 pages