{"paper":{"title":"M{\\\"o}bius orthogonality in density for zero entropy dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Alexander Gomilko, Mariusz Lema\\'nczyk, Thierry de la Rue (LMRS)","submitted_at":"2019-05-16T07:14:39Z","abstract_excerpt":"It is proved that whenever a zero entropy dynamical system $(X,T)$ has only countably many ergodic measures and $\\mu$ stands for the arithmetic M{\\\"o}bius function, then there exists  a subset $A$ of integers depending only on the system, of logarithmic density one, such that for each $f$ continuous on $X$, $\\frac1N \\sum_{n\\leq N} f(T^nx)\\mu(n) \\to 0$ as $N\\to\\infty$, $N\\in A$, uniformly in $x\\in X$. In particular, the density version of M{\\\"o}bius orthogonality holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06563","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"}