{"paper":{"title":"Correlations between real conjugate algebraic numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.NT","authors_text":"Dmitry Zaporozhets, Dzianis Kaliada, Friedrich G\\\"otze","submitted_at":"2015-10-02T09:19:59Z","abstract_excerpt":"For $B\\subset\\mathbb{R}^k$ denote by $\\Phi_k(Q;B)$ the number of ordered $k$-tuples in $B$ of real conjugate algebraic numbers of degree $\\leq n$ and naive height $\\leq Q$. We show that $$ \\Phi_k(Q;B) = \\frac{(2Q)^{n+1}}{2\\zeta(n+1)} \\int_{B} \\rho_k(\\mathbf{x})\\,d\\mathbf{x} + O\\left(Q^n\\right),\\quad Q\\to \\infty, $$ where the function $\\rho_k$ will be given explicitly. If $n=2$, then an additional factor $\\log Q$ appears in the reminder term."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00536","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"}