{"paper":{"title":"On the density of abelian l-extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chih-Yun Chuang, Yen-Liang Kuan","submitted_at":"2015-09-04T05:41:30Z","abstract_excerpt":"We derive an asymptotic formula which counts the number of abelian extensions of prime degrees over rational function fields. Specifically, let $\\ell$ be a rational prime and $K$ a rational function field $\\Bbb F_q(t)$ with $\\ell \\nmid q$. Let $\\textup{Disc}_f\\left(F/K\\right)$ denote the finite discriminant of $F$ over $K$. Denote the number of abelian $\\ell$-extensions $F/K$ with $\\textup{deg}\\left(\\textup{Disc}_f(F/K)\\right) = (\\ell-1)\\alpha n$ by $a_{\\ell}(n)$, where $\\alpha=\\alpha(q, \\ell)$ is the order of $q$ in the multiplicative group $\\left(\\Bbb Z/\\ell \\Bbb Z\\right)^\\times$. We give a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01345","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"}