{"paper":{"title":"Computing relative power integral bases in a family of quartic extensions of imaginary quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Borka Jadrijevi\\'c, Zrinka Franu\\v{s}i\\'c","submitted_at":"2016-07-11T18:11:56Z","abstract_excerpt":"Let $M$ be an imaginary quadratic field with the ring of integers $\\mathbb{Z}_{M}$ and let $\\xi$ be a root of polynomial $$f\\left( x\\right) =x^{4}-2cx^{3}+2x^{2}+2cx+1,$$ where $c\\in\\mathbb{Z}_{M},$ $c\\notin\\left\\{ 0,\\pm2\\right\\}$. We consider an infinite family of octic fields $K_{c}=M\\left( \\xi\\right)$ with the ring of integers $\\mathbb{Z}_{K_{c}}.$ Our goal is to determine all generators of relative power integral basis of $\\mathcal{O=}\\mathbb{Z}_{M}\\left[ \\xi\\right]$ over $\\mathbb{Z}_{M}.$ We show that our problem reduces to solving the system of relative Pellian equations \\[ cV^{2}-\\left("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03064","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"}