{"paper":{"title":"Lower bounds for covolumes of arithmetic lattices in $PSL_2(\\mathbb R)^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Amir D\\v{z}ambi\\'c","submitted_at":"2015-01-26T15:26:43Z","abstract_excerpt":"We study the covolumes of arithmetic lattices in $PSL_2(\\mathbb R)^n$ for $n\\geq 2$ and identify uniform and non-uniform irreducible lattices of minimal covolume. More precisely, let $\\mu$ be the Euler-Poincar\\'e measure on $PSL_2(\\mathbb R)^n$ and $\\chi=\\mu/2^n$. We show that the Hilbert modular group $PSL_2(\\mathfrak o_{k_{49}})\\subset PSL_2(\\mathbb R)^3$, with $k_{49}$ the totally real cubic field of discriminant $49$ has the minimal covolume with respect to $\\chi$ among all irreducible lattices in $PSL_2(\\mathbb R)^n$ for $n\\geq 2$ and is unique such lattice up to conjugation. The uniform "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06443","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"}