{"paper":{"title":"A more intuitive proof of a sharp version of Hal\\'asz's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adam J Harper, Andrew Granville, K. Soundararajan","submitted_at":"2017-06-12T17:46:00Z","abstract_excerpt":"We prove a sharp version of Hal\\'asz's theorem on sums $\\sum_{n \\leq x} f(n)$ of multiplicative functions $f$ with $|f(n)|\\le 1$. Our proof avoids the \"average of averages\" and \"integration over $\\alpha$\" manoeuvres that are present in many of the existing arguments. Instead, motivated by the circle method we express $\\sum_{n \\leq x} f(n)$ as a triple Dirichlet convolution, and apply Perron's formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03755","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"}