{"paper":{"title":"Automorphisms with quasi-discrete spectrum, multiplicative functions and average orthogonality along short intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"El Houcein El Abdalaoui (LMRS), Mariusz Lemanczyk, Thierry de la Rue (LMRS)","submitted_at":"2015-07-15T09:04:37Z","abstract_excerpt":"We show that Sarnak's conjecture on M\\\"obius disjointness holds in every uniquely ergodic modelof a quasi-discrete spectrum automorphism. A consequence of this result is that, for each non constant polynomial $P\\in\\R[x]$ with irrational leading coefficient and for each multiplicative function $\\bnu:\\N\\to\\C$, $|\\bnu|\\leq1$, we have\\[    \\frac{1}{M} \\sum\\_{M\\le m\\textless{}2M} \\frac{1}{H} \\left| \\sum\\_{m\\le n \\textless{} m+H} e^{2\\pi iP(n)}\\bnu(n)  \\right|\\longrightarrow  0  \\]  as $M\\to\\infty$, $H\\to\\infty$, $H/M\\to 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04132","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"}