{"paper":{"title":"Distribution of lattice orbits on homogeneous varieties","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexander Gorodnik, Barak Weiss","submitted_at":"2004-07-20T18:53:37Z","abstract_excerpt":"Given a lattice \\Gamma in a locally compact group G and a closed subgroup H of G, one has a natural action of \\Gamma on the homogeneous space V=H\\G. For an increasing family of finite subsets {\\Gamma_T: T>0}, a dense orbit v\\Gamma, v\\in V, and compactly supported function \\phi on V, we consider the sums\n  S_{\\phi,v}(T)=\\sum_{\\gamma\\in \\Gamma_T} \\phi(v \\gamma).\n Understanding the asymptotic behavior of S_{\\phi,v}(T) is a delicate problem which has only been considered for certain very special choices of H, G and {\\Gamma_T}. We develop a general abstract approach to the problem, and apply it to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407345","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"}