{"paper":{"title":"Some optimal links between generations of correlation averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Coppola, Maurizio Laporta","submitted_at":"2015-05-18T08:41:30Z","abstract_excerpt":"For a real-valued and essentially bounded arithmetic function $f$, i.e., $f(n)\\ll_{\\varepsilon}\\!n^{\\varepsilon},\\,\\forall\\varepsilon\\!>\\!0$, we \\enspace give some optimal links between non-trivial bounds for the sums $\\sum_{h\\le H}\\sum_{N<n\\le 2N}f(n)f(n-h)$, $\\sum_{N<x\\le 2N} \\big| \\sum_{x<n\\le x+H}f(n)\\big|^2$ and $\\sum_{N<n\\le 2N} \\big| \\sum_{0\\le |n-x|\\le H}\\big(1-{|n-x|\\over H}\\big)f(n)\\big|^2$, with $H=o(N)$ as $N\\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04551","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"}