{"paper":{"title":"Quantum Limits of Eisenstein Series in H^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Niko Laaksonen","submitted_at":"2015-11-23T20:45:48Z","abstract_excerpt":"We study the quantum limits of Eisenstein series off the critical line for $\\mathrm{PSL}_{2}(\\mathcal{O}_{K})\\backslash\\mathbb{H}^{3}$, where $K$ is an imaginary quadratic field of class number one. This generalises the results of Petridis, Raulf and Risager on $\\mathrm{PSL}_{2}(\\mathbb{Z})\\backslash\\mathbb{H}^{2}$. We observe that the measures $\\lvert E(p,\\sigma_{t}+it)\\rvert^{2}d\\mu(p)$ become equidistributed only if $\\sigma_{t}\\rightarrow 1$ as $t\\rightarrow\\infty$. We use these computations to study measures defined in terms of the scattering states, which are shown to converge to the abso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07411","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}