{"paper":{"title":"Cohen-Lenstra-Gerth Heuristics via Automorphism Counts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cam McLeman, Nathan Jones","submitted_at":"2017-12-28T23:09:30Z","abstract_excerpt":"For a finite abelian 2-group $G$, we study the frequency with which quadratic imaginary number fields $K$ have 2-part of their class group $K$ isomorphic to $G$. A philosophy enunciated by Gerth extends the Cohen-Lenstra heuristics for imaginary quadratic number fields to the case $p=2$, by referencing both the 2-rank and the 4-rank of the group in question. A recent paper by Smith provides relative density statements about the $2^{k+1}$-rank of such a class group given its $2^1$- through $2^k$-ranks, for $k \\geq 2$. We deduce from Smith's results an explicit automorphism-count-theoretic state"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10080","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":""},"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"}