{"paper":{"title":"The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ila Varma, Manjul Bhargava","submitted_at":"2014-01-23T05:22:11Z","abstract_excerpt":"We determine the mean number of 3-torsion elements in the class groups of quadratic orders, where the quadratic orders are ordered by their absolute discriminants. Moreover, for a quadratic order $\\mathcal{O}$ we distinguish between the two groups: $\\mathrm{Cl}_3(\\mathcal{O})$, the group of ideal classes of order $3$; and $\\mathcal{I}_3(\\mathcal{O})$, the group of ideals of order $3$. We determine the mean values of both $|\\mathrm{Cl}_3(\\mathcal{O})|$ and $|\\mathcal{I}_3(\\mathcal{O})|$, as $\\mathcal{O}$ ranges over any family of orders defined by finitely many (or in suitable cases, even infin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5875","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"}