{"paper":{"title":"On the average distribution of divisors of friable numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sary Drappeau","submitted_at":"2015-11-30T13:47:40Z","abstract_excerpt":"A number is said to be $y$-friable if it has no prime factor greater than $y$. In this paper, we prove a central limit theorem on average for the distribution of divisors of $y$-friable numbers less than $x$, for all $(x, y)$ satisfying $2\\leq y \\leq {\\rm e}^{(\\log x)/(\\log\\log x)^{1+\\varepsilon}}$. This was previously known under the additional constraint $y\\geq {\\rm e}^{(\\log\\log x)^{5/3+\\varepsilon}}$, by work of Basquin. Our argument relies on the two-variable saddle-point method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09305","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"}