{"paper":{"title":"On infinite multiplicative Sidon sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Csaba S\\'andor, P\\'eter P\\'al Pach","submitted_at":"2017-09-11T19:06:58Z","abstract_excerpt":"We prove that if $A$ is an infinite multiplicative Sidon set, then $\\liminf\\limits_{n\\to \\infty}\\frac{|A(n)|-\\pi (n)}{\\frac{n^{3/4}}{(\\log n)^3}}<\\infty$ and construct an infinite multiplicative Sidon set satisfying $\\liminf\\limits_{n\\to \\infty}\\frac{|A(n)|-\\pi (n)}{\\frac{n^{3/4}}{(\\log n)^3}}>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03550","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"}