{"paper":{"title":"On an asymptotic behavior of the divisor function $\\tau(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tigran Hakobyan","submitted_at":"2014-06-14T07:53:12Z","abstract_excerpt":"For $\\mu>0$ we study an asymptotic behavior of the sequence defined as $$T_{n}(\\mu)=\\frac{max_{1\\leq m \\leq {n^{\\frac{1}{\\mu}}}}\\{\\tau (n + m)\\}}{\\tau(n)},\\ n=1,2,...$$ where $\\tau(n)$ denotes the number of natural divisors of the given $n\\in \\mathbb{N}$. The motivation of this observation is to explore whether $\\tau$ function oscillates rapidly in small neighborhoods of natural numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3698","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":""},"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"}