{"paper":{"title":"M\\\"{o}bius disjointness for skew products on a circle and a nilmanifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Jianya Liu, Ke Wang, Wen Huang","submitted_at":"2019-07-03T04:43:27Z","abstract_excerpt":"Let $\\mathbb{T}$ be the unit circle and $\\Gamma \\backslash G$ the $3$-dimensional Heisenberg nilmanifold. We prove that a class of skew products on $\\mathbb{T} \\times \\Gamma \\backslash G$ are distal, and that the M\\\"{o}bius function is linearly disjoint from these skew products. This verifies the M\\\"{o}bius Disjointness Conjecture of Sarnak."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01735","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"}