{"paper":{"title":"Bertrand's Postulate for Number Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"M. Ram Murty, Thomas A. Hulse","submitted_at":"2015-08-04T19:49:24Z","abstract_excerpt":"Consider an algebraic number field, $K$, and its ring of integers, $\\mathcal{O}_K$. There exists a smallest $B_K>1$ such that for any $x>1$ we can find a prime ideal, $\\mathfrak{p}$, in $\\mathcal{O}_K$ with norm $N(\\mathfrak{p})$ in the interval $[x,B_Kx]$. This is a generalization of Bertrand's postulate to number fields, and in this paper we produce bounds on $B_K$ in terms of the invariants of $K$ from an effective prime ideal theorem due to Lagarias and Odlyzko. We also show that a bound on $B_K$ can be obtained from an asymptotic estimate for the number of ideals in $\\mathcal{O}_K$ less t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00887","kind":"arxiv","version":2},"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"}