{"paper":{"title":"Construction of class fields over cyclotomic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dong Sung Yoon, Ja Kyung Koo","submitted_at":"2012-03-21T07:11:43Z","abstract_excerpt":"Let $\\ell$ and $p$ be odd primes. For a positive integer $\\mu$ let $k_\\mu$ be the ray class field of $k=\\mathbb{Q}(e^{2\\pi i/\\ell})$ modulo $2p^\\mu$. We present certain class fields $K_\\mu$ of $k$ such that $k_\\mu\\leq K_\\mu\\leq k_{\\mu+1}$, and find the degree of $K_\\mu/k_\\mu$ explicitly. And we also construct, in the sense of Hilbert, primitive generators of the field $K_\\mu$ over $k_\\mu$ by using Shimura's reciprocity law and special values of theta constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4662","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"}