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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("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1405.4747","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-19T14:37:19Z","cross_cats_sorted":[],"title_canon_sha256":"4f057a2d3970849845225561d8a1a24d34a24013549b76786c2208f4f0775655","abstract_canon_sha256":"b9d862c960f4c2967639f79af754bee6b0718a0aebd8ebdf595bb139e50cd620"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:14.398088Z","signature_b64":"+v78sJ3PDsPwTruXYPnWR8tN9fAcTc+dsNdsYyXuDl2shYEe6DQycEmz8MkfYTUM3TMVvmhiwEndYm2d98P5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"323c4aebac30b80516c85f9db79c9753eb6b2631de2712d2cc5304559f7cda24","last_reissued_at":"2026-05-17T23:53:14.397538Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:14.397538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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