{"paper":{"title":"Determination of the Fricke families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dong Hwa Shin, Ick Sun Eum","submitted_at":"2015-01-17T11:59:37Z","abstract_excerpt":"For a positive integer $N$ divisible by $4$, let $\\mathcal{O}^1_N(\\mathbb{Q})$ be the ring of weakly holomorphic modular functions for the congruence subgroup $\\Gamma^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring $\\mathcal{O}^1_N(\\mathbb{Q})$ over $\\mathbb{Q}$, from which we are able to classify all Fricke families of such level $N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04193","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"}