{"paper":{"title":"On the density function of the distribution of real algebraic numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dzianis Kaliada","submitted_at":"2014-05-07T14:46:46Z","abstract_excerpt":"In this paper we study the distribution of the real algebraic numbers. Given an interval $I$, a positive integer $n$ and $Q>1$, define the counting function $\\Phi_n(Q;I)$ to be the number of algebraic numbers in $I$ of degree $n$ and height $\\le Q$. Let $I_x = (-\\infty,x]$. The distribution function is defined to be the limit (as $Q\\to\\infty$) of $\\Phi_n(Q;I_x)$ divided by the total number of real algebraic numbers of degree $n$ and height $\\le Q$. We prove that the distribution function exists and is continuously differentiable. We also give an explicit formula for its derivative (to be refer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1627","kind":"arxiv","version":5},"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"}