{"paper":{"title":"On the Fourier-Walsh Spectrum on the Moebius Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean Bourgain","submitted_at":"2011-12-06T21:18:16Z","abstract_excerpt":"We study the Fourier-Walsh spectrum $\\{\\hat\\mu (S); S\\subset\\{1, ..., n\\}\\}$ of the Moebius function $\\mu$ restricted to $\\{0, 1, 2, ..., 2^n-1\\}\\simeq \\{0, 1\\}^n$ and prove that it is not captued by levels \\{\\hat\\mu (S)| \\, |S|< n^{\\frac 23-\\epsion}\\}. An application to correlation with monotone Boelean functions is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1423","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"}