{"paper":{"title":"Mutliple mixing and disjointness for time changes of bounded-type Heisenberg nilflows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Kanigowski, Giovanni Forni","submitted_at":"2018-10-31T14:55:17Z","abstract_excerpt":"We study time changes of bounded type Heisenberg nilflows $(\\phi_t)$ acting on the Heisenberg nilmanifold $M$. We show that for every positive $\\tau\\in W^s(M)$, $s~>~7/2$, every non-trivial time change $(\\phi_t^{\\tau})$ enjoys the Ratner property. As a consequence every mixing time change is mixing of all orders. Moreover we show that for every $\\tau\\in W^s(M)$, $s>9/2$ and every $p,q\\in \\mathbb{N}$, $p\\neq q$, $(\\phi_{pt}^\\tau)$ and $(\\phi_{qt}^\\tau)$ are disjoint. As a consequence Sarnak's Conjecture on M\\\"obius disjointness holds for all such time changes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13319","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"}