{"paper":{"title":"On Bhargava's heuristics for $\\mathbf{GL}_2(\\mathbb{F}_p)$-number fields and the number of elliptic curves of bounded conductor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Lipnowski","submitted_at":"2016-10-29T07:14:50Z","abstract_excerpt":"We propose a new model for counting $\\mathbf{GL}_2(\\mathbb{F}_p)$-number fields having the same local properties as the splitting field of the mod $p$-Galois representation associated with an elliptic curve over the rational numbers. We explain how this new model and Bhargava's local-to-global heuristics for counting $\\mathbf{GL}_2(\\mathbb{F}_p)$-number fields both shed light on the problem of estimating the number of elliptic curves over the rational numbers of squarefree conductor $N < X.$\n  The new model predicts the existence of significantly more $\\mathbf{GL}_2(\\mathbb{F}_p)$-number field"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09467","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"}