{"paper":{"title":"The average sizes of two-torsion subgroups in quotients of class groups of cubic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zev Klagsbrun","submitted_at":"2017-01-11T03:23:54Z","abstract_excerpt":"We prove a generalization of a result of Bhargava regarding the average size $\\mathrm{Cl}(K)[2]$ as $K$ varies among cubic fields. For a fixed set of rational primes $S$, we obtain a formula for the average size of $\\mathrm{Cl}(K)/\\langle S \\rangle[2]$ as $K$ varies among cubic fields with a fixed signature, where $\\langle S \\rangle$ is the subgroup of $\\mathrm{Cl}(K)$ generated by the classes of primes of $K$ above primes in $S$.\n  As a consequence, we are able to calculate the average sizes of $K_{2n}(\\mathcal{O}_K)[2]$ for $n > 0$ and for the relaxed Selmer group $\\mathrm{Sel}_2^S(K)$ as $K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02838","kind":"arxiv","version":3},"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"}