{"paper":{"title":"On generalized Thue-Morse functions and their values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dzmitry Badziahin, Evgeny Zorin","submitted_at":"2015-09-01T13:50:08Z","abstract_excerpt":"This paper naturally extends and generalizes our previous work \"Thue-Morse constant is not badly approximable\", arXiv:1407.3182 [math.NT]. Here we consider the Laurent series $f_d(x) = \\prod_{n=0}^\\infty (1 - x^{-d^n})$, $d\\in\\mathbb{N}$, $d\\geq 2$ which generalize the generating function $f_2(x)$ of the Thue-Morse number, and study their continued fraction expansion. In particular, we show that the convergents of $x^{-d+1}f_d(x)$ have quite a regular structure. We address as well the question whether the corresponding Mahler numbers $f_d(a)\\in\\mathbb{R}$, $a,d\\in\\mathbb{N}$, $a,d\\geq 2$, are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00297","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"}