{"paper":{"title":"On the dimension spectrum of infinite subsystems of continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Dmitriy Leykekhman, Mariusz Urba\\'nski, Vasileios Chousionis","submitted_at":"2018-05-30T11:17:54Z","abstract_excerpt":"In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if $E$ is any arithmetic progression, the set of primes, or the set of squares $\\{n^2\\}_{n \\in \\mathbb{N}}$, then the continued fractions whose digits lie in $E$ have full dimension spectrum, which we denote by $DS(\\mathcal{CF}_E)$. Moreover we prove that if $E$ is an infinite set of consecutive powers then the dimension spectrum $DS(\\mathcal{CF}_E)$ always contains a non trivial interval. We also show that there exists some $E \\subset \\mathbb{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11904","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"}