{"paper":{"title":"Distribution of real algebraic integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dzianis Kaliada","submitted_at":"2014-07-10T16:50:29Z","abstract_excerpt":"In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their naive height tends to infinity. Let $I \\subset \\mathbb{R}$ be an arbitrary bounded interval, and $Q$ be a sufficiently large number. We obtain an asymptotic formula for the count of algebraic integers $\\alpha$ of fixed degree $n$ and naive height $H(\\alpha)\\le Q$ lying in $I$. In this formula, we estimate the order of the error term from above and below. We show that algebraic integers of degree $n$ are distributed asymptotically like algebraic numbers of degree $(n-1)$ as the upper bound $Q$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2861","kind":"arxiv","version":4},"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"}