{"paper":{"title":"Continued fractions of certain Mahler functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dmitry Badziahin","submitted_at":"2017-02-24T03:56:14Z","abstract_excerpt":"We investigate the continued fraction expansion of the infinite products $g(x) = x^{-1}\\prod_{t=0}^\\infty P(x^{-d^t})$ where polynomials $P(x)$ satisfy $P(0)=1$ and $\\deg(P)<d$. We construct relations between partial quotients of $g(x)$ which can be used to get recurrent formulae for them. We provide that formulae for the cases $d=2$ and $d=3$. As an application, we prove that for $P(x) = 1+ux$ where $u$ is an arbitrary rational number except 0 and 1, and for any integer $b$ with $|b|>1$ such that $g(b)\\neq0$ the irrationality exponent of $g(b)$ equals two. In the case $d=3$ we provide a parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07457","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"}