{"paper":{"title":"Algebraic Numbers, Hyperbolicity, and Density Modulo One","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Alexander Gorodnik, Shirali Kadyrov","submitted_at":"2011-09-01T13:18:29Z","abstract_excerpt":"We prove the density of the sets of the form ${{\\lambda}_1^m {\\mu}_1^n {\\xi}_1 +...+{\\lambda}_k^m {\\mu}_k^n {\\xi}_k : m,n \\in \\mathbb N}$ modulo one, where $\\lambda_i$ and $\\mu_i$ are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelean groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0183","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"}