{"paper":{"title":"Intrinsic Diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.NT","authors_text":"Anton Lukyanenko, Joseph Vandehey","submitted_at":"2015-10-20T20:06:12Z","abstract_excerpt":"We initiate the study of an intrinsic notion of Diophantine approximation on a rational Carnot group $G$. If $G$ has Hausdorff dimension $Q$, we show that its Diophantine exponent is equal to $(Q+1)/Q$, generalizing the case $G=\\mathbb R^n$. We furthermore obtain a precise asymptotic on the count of rational approximations.\n  We then focus on the case of the Heisenberg group $\\mathbb H^n$, distinguishing between two notions of Diophantine approximation by rational points in $\\mathbb H^n$: Carnot Diophantine approximation and Siegel Diophantine approximation.\n  After computing the Siegel Diopha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06033","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"}