{"paper":{"title":"On Correlations of Liouville-like Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yichen You","submitted_at":"2023-12-10T21:52:46Z","abstract_excerpt":"Let $\\mathcal{A}$ be a set of mutually coprime positive integers, satisfying \\begin{align*}\n  \\sum\\limits_{a\\in\\mathcal{A}}\\frac{1}{a} = \\infty. \\end{align*} Define the (possibly non-multiplicative) \"Liouville-like\" functions \\begin{align*}\n  \\lambda_{\\mathcal{A}}(n) = (-1)^{\\#\\{a:a|n, a \\in \\mathcal{A}\\}} \\text{ or } (-1)^{\\#\\{a:a^\\nu\\parallel n, a \\in \\mathcal{A}, \\nu \\in \\mathbb{N}\\}}. \\end{align*} We show that \\begin{align*}\n  \\lim\\limits_{x\\to\\infty}\\frac{1}{x}\\sum\\limits_{n \\leq x} \\lambda_\\mathcal{A}(n) = 0 \\end{align*} holds, answering a question of de la Rue."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.06012","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.06012/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}