{"paper":{"title":"Subexponentially increasing sums of partial quotients in continued fraction expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lingmin Liao (LAMA), Michal Rams (PAN)","submitted_at":"2014-05-19T14:37:19Z","abstract_excerpt":"We investigate from a multifractal analysis point of view the increasing rate of the sums of partial quotients $S\\_n(x)=\\sum\\_{j=1}^n a\\_j(x)$, where $x=[a\\_1(x), a\\_2(x), \\cdots ]$ is the continued fraction expansion of an irrational $x\\in (0,1)$.  Precisely, for an increasing function $\\varphi: \\mathbb{N} \\rightarrow \\mathbb{N}$, one is interested in the Hausdorff dimension of the sets\\[E\\_\\varphi = \\left\\{x\\in (0,1): \\lim\\_{n\\to\\infty} \\frac {S\\_n(x)} {\\varphi(n)} =1\\right\\}.\\]Several cases are solved by Iommi and Jordan, Wu and Xu, and Xu. We attack the remaining subexponential case $\\exp("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4747","kind":"arxiv","version":3},"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"}