{"paper":{"title":"Effect of monogenicity on $2$-torsion in the class group of number fields of odd degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Artane Siad","submitted_at":"2020-11-17T18:53:49Z","abstract_excerpt":"We study average $2$-torsion in the class group of monogenised fields of odd degree. Bhargava-Hanke-Shankar have recently shown that the average number of non-trivial $2$-torsion elements in the class group of monogenised cubic fields of a fixed signature is twice the value predicted by the Cohen-Lenstra-Martinet-Malle heuristic for the full family. Fix any odd degree $n$ and signature $(r_{1},r_{2})$. In this work, we prove that the average number of non-trivial elements in the class group of monogenised fields of degree $n$ and signature $(r_{1},r_{2})$ is bounded by twice the value predicte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.08834","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.08834/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}