{"paper":{"title":"A remark on the extreme value theory for continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kunkun Song, Lulu Fang","submitted_at":"2016-08-15T16:55:13Z","abstract_excerpt":"Let $x$ be a irrational number in the unit interval and denote by its continued fraction expansion $[a_1(x), a_2(x), \\cdots, a_n(x), \\cdots]$. For any $n \\geq 1$, write $T_n(x) = \\max_{1 \\leq k \\leq n}\\{a_k(x)\\}$. We are interested in the Hausdorff dimension of the fractal set \\[ E_\\phi = \\left\\{x \\in (0,1): \\lim_{n \\to \\infty} \\frac{T_n(x)}{\\phi(n)} =1\\right\\}, \\] where $\\phi$ is a positive function defined on $\\mathbb{N}$ with $\\phi(n) \\to \\infty$ as $n \\to \\infty$. Some partial results have been obtained by Wu and Xu, Liao and Rams, and Ma. In the present paper, we further study this topic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04326","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"}