{"paper":{"title":"On the Divergence of the Rogers-Ramanujan Continued Fraction on the Unit Circle","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Doug Bowman, Jimmy Mc Laughlin","submitted_at":"2001-07-06T04:14:18Z","abstract_excerpt":"Let the continued fraction expansion of any irrational number $t \\in (0,1)$ be denoted by $[0,a_{1}(t),a_{2}(t),...]$ and let the i-th convergent of this continued fraction expansion be denoted by $c_{i}(t)/d_{i}(t)$. Let \\[ S=\\{t \\in (0,1): a_{i+1}(t) \\geq \\phi^{d_{i}(t)} \\text{infinitely often}\\}, \\] where $\\phi = (\\sqrt{5}+1)/2$. Let $Y_{S} =\\{\\exp(2 \\pi i t): t \\in S \\}$. It is shown that if $y \\in Y_{S}$ then the Rogers-Ramanujan continued fraction, R(y), diverges at y. S is an uncountable set of measure zero. It is also shown that there is an uncountable set of points, $G \\subset Y_{S}$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107043","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"}