{"paper":{"title":"On the multiplicative Erd\\H{o}s discrepancy problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Coons","submitted_at":"2010-03-28T18:36:19Z","abstract_excerpt":"As early as the 1930s, P\\'al Erd\\H{o}s conjectured that: {\\em for any multiplicative function $f:\\mathbb{N}\\to\\{-1,1\\}$, the partial sums $\\sum_{n\\leq x}f(n)$ are unbounded.} Considering this conjecture, in this paper we consider multiplicative functions $f$ satisfying $$\\sum_{p\\leq x}f(p)=c\\cdot\\frac{x}{\\log x}(1+o(1)).$$ We prove that if $c>0$ then the partial sums of $f$ are unbounded, and if $c<0$ then the partial sums of $\\mu f$ are unbounded. Extensions of this result are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5388","kind":"arxiv","version":4},"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"}