{"paper":{"title":"Lattice deformations in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ioannis Konstantoulas, Jayadev S. Athreya","submitted_at":"2015-10-06T05:09:37Z","abstract_excerpt":"The space of deformations of the integer Heisenberg group under the action of $\\textrm{Aut}(H(\\mathbb{R}))$ is a homogeneous space for a non-reductive group. We analyze its structure as a measurable dynamical system and obtain mean and variance estimates for Heisenberg lattice point counting in measurable subsets of $\\mathbb{R}^3$; in particular, we obtain a random Minkowski-type theorem. Unlike the Euclidean case, we show there are necessary geometric conditions on the sets that satisfy effective variance bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01433","kind":"arxiv","version":2},"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"}