{"paper":{"title":"Pointwise equidistribution with an error rate and with respect to unbounded functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Barak Weiss, Dmitry Kleinbock, Ronggang Shi","submitted_at":"2015-05-25T19:01:55Z","abstract_excerpt":"Consider $G=\\SL_{ d }(\\mathbb R)$ and $ \\Gamma=\\SL_{ d }(\\mathbb Z)$. It was recently shown by the second-named author \\cite{s} that for some diagonal subgroups $\\{g_t\\}\\subset G$ and unipotent subgroups $U\\subset G$, $g_t$-trajectories of almost all points on all $U$-orbits on $G/\\Gamma$ are equidistributed with respect to continuous compactly supported functions $\\varphi$ on $G/\\Gamma$. In this paper we strengthen this result in two directions: by exhibiting an error rate of equidistribution when $\\varphi$ is smooth and compactly supported, and by proving equidistribution with respect to cer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06717","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"}