{"paper":{"title":"On the Distribution of 2-Selmer ranks of Quadratic Twists of Elliptic Curves over $\\mathbb{Q}$","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinzhao Pan, Ye Tian","submitted_at":"2025-03-27T12:52:42Z","abstract_excerpt":"We characterize the distribution of 2-Selmer ranks of quadratic twists of elliptic curves over $\\mathbb{Q}$ with full rational 2-torsion. We propose a new type of random alternating matrix model $M_{*,\\mathbf t}^{\\mathrm{Alt}}(\\mathbb{F}_2)$ over $\\mathbb{F}_2$ with 0, 1 or 2 ``holes'', with associated Markov chains, described by parameter $\\mathbf t=(t_1,\\cdots,t_s)\\in\\mathbb{Z}^s$ where $s$ is the number of ``holes''. We proved that for each equivalence classes of quadratic twists of elliptic curves:\n  (1) The distribution of 2-Selmer ranks agrees with the distribution of coranks of matrices"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21462","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.21462/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"}