{"paper":{"title":"A strictly ergodic, positive entropy subshift uniformly uncorrelated to the Moebius function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jacek Serafin, Tomasz Downarowicz","submitted_at":"2019-02-11T21:55:52Z","abstract_excerpt":"A recent result of Downarowicz and Serafin (DS) shows that there exist positive entropy subshifts satisfying the assertion of Sarnak's conjecture. More precisely, it is proved that if $y=(y_n)_{n\\ge 1}$ is a bounded sequence with zero average along every infinite arithmetic progression (the M\\\"obius function is an example of such a \\sq\\ $y$) then for every $N\\ge 2$ there exists a subshift $\\Sigma$ over $N$ symbols, with entropy arbitrarily close to $\\log N$, uncorrelated to $y$.\n  In the present note, we improve the result of (DS). First of all, we observe that the uncorrelation obtained in (D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04162","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"}