{"paper":{"title":"On a problem of countable expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Derong Kong, Yuru Zou","submitted_at":"2015-03-25T16:03:22Z","abstract_excerpt":"For a real number $q\\in(1,2)$ and $x\\in[0,1/(q-1)]$, the infinite sequence $(d_i)$ is called a \\emph{$q$-expansion} of $x$ if $$ x=\\sum_{i=1}^\\infty\\frac{d_i}{q^i},\\quad d_i\\in\\{0,1\\}\\quad\\textrm{for all}~ i\\ge 1. $$ For $m=1, 2, \\cdots$ or $\\aleph_0$ we denote by $\\mathcal{B}_m$ the set of $q\\in(1,2)$ such that there exists $x\\in[0,1/(q-1)]$ having exactly $m$ different $q$-expansions. It was shown by Sidorov (2009) that $q_2:=\\min \\mathcal{B}_2\\approx1.71064$, and later asked by Baker (2015) whether $q_2\\in\\mathcal{B}_{\\aleph_0}$? In this paper we provide a negative answer to this question a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07434","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"}