{"paper":{"title":"M\\\"obius disjointness for models of an ergodic system and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"el Houcein el Abdalaoui, Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk, Thierry de la Rue","submitted_at":"2017-04-11T19:30:32Z","abstract_excerpt":"Given a topological dynamical system $(X,T)$ and an arithmetic function $\\boldsymbol{u}\\colon\\mathbb{N}\\to\\mathbb{C}$, we study the strong MOMO property (relatively to $\\boldsymbol{u}$) which is a strong version of $\\boldsymbol{u}$-disjointness with all observable sequences in $(X,T)$. It is proved that, given an ergodic measure-preserving system $(Z,\\mathcal{D},\\kappa,R)$, the strong MOMO property (relatively to $\\boldsymbol{u}$) of a uniquely ergodic model $(X,T)$ of $R$ yields all other uniquely ergodic models of $R$ to be $\\boldsymbol{u}$-disjoint. It follows that all uniquely ergodic mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03506","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"}