{"paper":{"title":"The Moebius function and continuous extensions of rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk","submitted_at":"2013-10-09T17:06:29Z","abstract_excerpt":"Let $f\\colon \\mathbb{T}\\to \\mathbb{R}$ be of class $C^{1+\\delta}$ for some $\\delta>0$ and let $c\\in\\mathbb{Z}$. We show that for a generic $\\alpha\\in\\mathbb{R}$, the extension $T_{c,f}\\colon \\mathbb{T}^2\\to\\mathbb{T}^2$ of the irrational rotation $Tx=x+\\alpha$, given by $T_{c,f}(x,u)=(x+\\alpha, u+cx+f(x))$ ($\\bmod\\ 1$) satisfies Sarnak's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2546","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"}