{"paper":{"title":"The least prime ideal in a given ideal class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Naser T. Sardari","submitted_at":"2018-02-17T04:58:02Z","abstract_excerpt":"Let $K$ be a number field with the discriminant $D_K$ and the class number $h_{K}$, which has bounded degree over $\\mathbb{Q}$. By assuming GRH, we prove that every ideal class of $K$ contains a prime ideal with norm less than $h_{K}^2\\log(D_K)^{2}$ and also all but $o(h_K)$ of them have a prime ideal with norm less than $h_{K}\\log(D_K)^{2+\\epsilon}$. For imaginary quadratic fields $K=\\mathbb{Q}(\\sqrt{D})$, by assuming Conjecture~\\ref{piarcor} (a weak version of the pair correlation conjecure), we improve our bounds by removing a factor of $\\log(D)$ from our bounds and show that these bounds a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06193","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"}