{"paper":{"title":"M\\\"obius Disjointness for Nilsequences Along Short Intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Xiaoguang He, Zhiren Wang","submitted_at":"2019-05-08T01:51:25Z","abstract_excerpt":"For a nilmanifold $G/\\Gamma$, a $1$-Lipschitz continuous function $F$ and the M\\\"obius sequence $\\mu(n)$, we prove a bound on the decay of the averaged short interval correlation $$\\frac1{HN}\\sum_{n\\leq N}\\Big|\\sum_{h\\leq H} \\mu(n+h)F(g^{n+h}x)\\Big|$$ as $H,N\\to\\infty$. The bound is uniform in $g\\in G$, $x\\in G/\\Gamma$ and $F$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02864","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"}