{"paper":{"title":"Discriminants of simplest 3^n-tic extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"T. Alden Gassert","submitted_at":"2014-09-27T18:53:07Z","abstract_excerpt":"Let $\\ell>2$ be a positive integer, $\\zeta_\\ell$ a primitive $\\ell$-th root of unity, and $K$ a number field containing $\\zeta_\\ell+\\zeta_\\ell^{-1}$ but not $\\zeta_\\ell$. In a recent paper, Chonoles et. al. study iterated towers of number fields over $K$ generated by the generalized Rikuna polynomial, $r_n(x,t;\\ell) \\in K(t)[x]$. They note that when $K = \\mathbb{Q}$, $t \\in \\{0,1\\}$, and $\\ell=3$, the only ramified prime in the resulting tower is 3, and they ask under what conditions is the number of ramified primes small. In this paper, we apply a theorem of Gu\\`ardia, Montes, and Nart to der"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7829","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"}