{"paper":{"title":"On the Joint Distribution Of $\\mathrm{Sel}_\\phi(E/\\mathbb{Q})$ and $\\mathrm{Sel}_{\\hat\\phi}(E^\\prime/\\mathbb{Q})$ in Quadratic Twist Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Kane, Zev Klagsbrun","submitted_at":"2017-02-09T03:13:22Z","abstract_excerpt":"If $E$ is an elliptic curve with a point of order two, then work of Klagsbrun and Lemke Oliver shows that the distribution of $\\dim_{\\mathbb{F}_2}\\mathrm{Sel}_\\phi(E^d/\\mathbb{Q}) - \\dim_{\\mathbb{F}_2} \\mathrm{Sel}_{\\hat\\phi}(E^{\\prime d}/\\mathbb{Q})$ within the quadratic twist family tends to the discrete normal distribution $\\mathcal{N}(0,\\frac{1}{2} \\log \\log X)$ as $X \\rightarrow \\infty$.\n  We consider the distribution of $\\mathrm{dim}_{\\mathbb{F}_2} \\mathrm{Sel}_\\phi(E^d/\\mathbb{Q})$ within such a quadratic twist family when $\\dim_{\\mathbb{F}_2} \\mathrm{Sel}_\\phi(E^d/\\mathbb{Q}) - \\dim_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02687","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"}