{"paper":{"title":"Upper and lower fast Khintchine spectra in continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Lingmin Liao (LAMA), Michal Rams (PAN)","submitted_at":"2014-06-04T19:06:38Z","abstract_excerpt":"For an irrational number $x\\in [0,1)$, let $x=[a\\_1(x), a\\_2(x),\\cdots]$ be its continued fraction expansion. Let $\\psi : \\mathbb{N} \\rightarrow \\mathbb{N}$ be a function with $\\psi(n)/n\\to \\infty$ as $n\\to\\infty$. The (upper, lower) fast Khintchine spectrum for $\\psi$ is defined as the Hausdorff dimension of the set of numbers $x\\in (0,1)$ for which the (upper, lower) limit of $\\frac{1}{\\psi(n)}\\sum\\_{j=1}^n\\log a\\_j(x)$ is equal to $1$. The fast Khintchine spectrum was determined by Fan, Liao, Wang, and Wu. We calculate the upper and lower fast Khintchine spectra. These three spectra can be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1148","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"}