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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.01345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-04T05:41:30Z","cross_cats_sorted":[],"title_canon_sha256":"040d661e9079daef0c2675236817ac9f5e9be34f72fc8a5cae93c1a6e88c1f7e","abstract_canon_sha256":"9a16cd8feb8b744ed0268f335c39ac09b4cb224033dc2bc0c869420403e9bf76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:57.933135Z","signature_b64":"vkkJp6l5JqL8S57I+VZnDH9oskKvlKV7xxzaANOt5pxlbOAqLv5ecDWTkqP7OlQobzsIy35Et5r6xjCVHzaaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e806a944093fd02ddfb9017946ec571d5c940a346d8b6b67679382ff50374a5b","last_reissued_at":"2026-05-18T01:33:57.932649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:57.932649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\left(\\Bbb Z/\\ell \\Bbb Z\\right)^\\times$. 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