{"paper":{"title":"Correlations of multiplicative functions with their partial sums","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gordon Chavez","submitted_at":"2024-09-03T17:58:50Z","abstract_excerpt":"Let $\\zeta(.)$ denote the Riemann zeta function and let $a(.)$ and $A(.)$ respectively denote a multiplicative function and its corresponding summatory function. We consider the correlation $$ \\langle a(n)A(n-1) \\rangle (T) = \\frac{1}{\\zeta(1+\\delta(T))}\\sum_{n\\leq T^{1-c}}\\frac{a(n)A(n-1)}{n^{1+\\delta(T)}} $$ where $0<c<1$ is arbitrary and $0<\\delta(T)=O\\left(T^{c-1}\\right)$ is suitably chosen. Let $\\mu(.)$ and $\\lambda(.)$ denote the M\\\"obius function and the Liouville function respectively while $M(.)$ and $L(.)$ denote their corresponding summatory functions. Under the Riemann hypothesis a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02106","kind":"arxiv","version":10},"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"}