{"paper":{"title":"A cubic nonconventional ergodic average with multiplicative or Mangoldt weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CV","math.NT","math.PR"],"primary_cat":"math.DS","authors_text":"el Houcein el Abdalaoui, Xiangdong Ye","submitted_at":"2016-06-17T19:25:50Z","abstract_excerpt":"We show that the cubic nonconventional ergodic averages of any order with a bounded multiplicative function weight converge almost surely to zero provided that the multiplicative function satisfies a strong Daboussi-Delange condition. We further obtain that the Ces\\`{a}ro mean of the self-correlations and some moving average of the self-correlations of such multiplicative functions converge to zero. Our proof gives, for any $N \\geq 2$, $$\\frac1{N}\\sum_{m=1}^{N}\\Big|\\frac1{N}\\sum_{n=1}^{N} \\bnu(n) \\bnu(n+m)\\Big| \\leq \\frac{C}{\\log(N)^{\\epsilon}},$$ and $$\\frac1{N^2}\\sum_{n,p=1}^{N}\\Big|\\frac1{N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05630","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"}