{"paper":{"title":"Thue-Morse constant is not badly approximable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dzmitry Badziahin, Evgeniy Zorin","submitted_at":"2014-07-11T14:57:21Z","abstract_excerpt":"We prove that Thue-Morse constant $\\tau_{TM}=0.01101001..._2$ is not a badly approximable number. Moreover, we prove that $\\tau_{TM}(a)=0.01101001..._a$ is not badly approximable for every integer base $a\\geq 2$ such that $a$ is not divisible by 15. At the same time we provide a precise formula for convergents of the Laurent series $\\tilde{f}_{TM}(z) = z^{-1}\\prod_{n=1}^\\infty (1-z^{-2^n})$, thus developing further the research initiated by Alf van der Poorten and others."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3182","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"}