{"paper":{"title":"On the fast Khintchine spectrum in continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bao-Wei Wang, Fan Ai-Hua (LAMFA), Jun Wu, Lingmin Liao (LAMA)","submitted_at":"2012-08-09T07:04:11Z","abstract_excerpt":"For $x\\in [0,1)$, let $x=[a_1(x), a_2(x),...]$ be its continued fraction expansion with partial quotients ${a_n(x), n\\ge 1}$. Let $\\psi : \\mathbb{N} \\rightarrow \\mathbb{N}$ be a function with $\\psi(n)/n\\to \\infty$ as $n\\to \\infty$. In this note, the fast Khintchine spectrum, i.e., the Hausdorff dimension of the set $$ E(\\psi):=\\Big{x\\in [0,1): \\lim_{n\\to\\infty}\\frac{1}{\\psi(n)}\\sum_{j=1}^n\\log a_j(x)=1\\Big} $$ is completely determined without any extra condition on $\\psi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1825","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"}