{"paper":{"title":"Coding of geodesics on some modular surfaces and applications to odd and even continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Claire Merriman, Florin P. Boca","submitted_at":"2017-11-19T04:28:38Z","abstract_excerpt":"The connection between geodesics on the modular surface $\\operatorname{PSL}(2,{\\mathbb Z})\\backslash {\\mathbb H}$ and regular continued fractions, established by Series, is extended to a connection between geodesics on $\\Gamma\\backslash {\\mathbb H}$ and odd and grotesque continued fractions, where $\\Gamma\\cong {\\Bbb Z}_3 \\ast {\\Bbb Z}_3$ is the index two subgroup of $\\operatorname{PSL}(2,{\\mathbb Z})$ generated by the order three elements $\\left( \\begin{smallmatrix} 0 & -1 \\\\ 1 & 1 \\end{smallmatrix} \\right)$ and $\\left( \\begin{smallmatrix} 0 & 1 \\\\ -1 & 1 \\end{smallmatrix} \\right)$, having an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06965","kind":"arxiv","version":5},"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"}