{"paper":{"title":"On small univoque bases of real numbers","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Derong Kong","submitted_at":"2016-02-19T15:05:58Z","abstract_excerpt":"Given a positive real number $x$, we consider the smallest base $q_s(x)\\in(1,2)$ for which there exists a unique sequence $(d_i)$ of zeros and ones such that \\[ x=\\sum_{i=1}^\\infty\\frac{d_i}{(q_s(x))^i}. \\] In this paper we give complete characterizations of those $x$'s for which $q_s(x)\\le q_{KL}$, where $q_{KL}$ is the Komornik-Loreti constant. Furthermore, we show that $q_s(x)=q_{KL}$ if and only if \\[ x\\in\\left\\{1, ~\\frac{q_{KL}}{q_{KL}^2-1},~ \\frac{1}{q_{KL}^2-1}, ~\\frac{1}{q_{KL}(q_{KL}^2-1)}\\right\\}. \\]\n  Finally, we determine the explicit value of $q_s(x)$ if $q_s(x)<q_{KL}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06173","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"}