{"paper":{"title":"Arithmetical properties of real numbers related to beta-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hajime Kaneko","submitted_at":"2017-08-10T06:43:54Z","abstract_excerpt":"The main purpose of this paper is to study the arithmetical properties of values \\(\\sum_{m=0}^{\\infty} \\beta^{-w(m)}\\), where \\(\\beta\\) is a fixed Pisot or Salem number and \\(w(m)\\) (\\(m=0,1,\\ldots\\)) are distinct sequences of nonnegative integers with \\(w(m+1)>w(m)\\) for any sufficiently large \\(m\\). We first introduce criteria for the algebraic independence of such values. Our criteria are applicable to certain sequences \\(w(m)\\) (\\(m=0,1,\\ldots\\)) with \\(\\lim_{m\\to\\infty}w(m+1)/w(m)=1.\\) For example, we prove that two numbers \\[\\sum_{m=1}^{\\infty}\\beta^{-\\lfloor \\varphi(1,0;m)\\rfloor}, \\sum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03093","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"}