{"paper":{"title":"Moments of unramified 2-group extensions of quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack Klys","submitted_at":"2017-10-02T17:03:45Z","abstract_excerpt":"Let $f\\left(K\\right)$ be the number of unramified extensions $L/K$ of a quadratic number field $K$ with $\\mathrm{Gal}\\left(L/K\\right)=H$ and $\\mathrm{Gal}\\left(L/\\mathbb{Q}\\right)=G$ where $G$ is a central extension of $\\mathbb{F}_{2}^{n}$ by $\\mathbb{F}_{2}$. We find a function $g\\left(K\\right)$ such that $f/g$ has finite moments and a distribution on its values. We show this distribution is a point mass when $H$ is non-abelian and the Cohen-Lenstra distribution when $H$ is abelian, despite the fact that the set of values of $f/g$ do not form a discrete set. We prove an explicit formula for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00793","kind":"arxiv","version":3},"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"}