{"paper":{"title":"Croissance asymptotique de nombres de Weil appartenant \\`a un corps de nombres fix\\'e","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"John Boxall","submitted_at":"2017-11-12T11:50:07Z","abstract_excerpt":"We prove an asymptotic formula as $x\\to +\\infty$ for the number of algebraic integers $\\alpha$ belonging to a fixed CM number field and satisfying $\\alpha\\overline{\\alpha}\\leq x$. This problem is related to the height zeta function $Z_h(X^K,s)$ associated to the anticanonical class of a certain toric variety $X^K$ over $\\mathbb{Q}$ and we show that $Z_h(X^K,s)$ has a meromorphic continuation to the half-plane $\\{\\Re(s)>\\frac{1}{2}\\}$ where it is holomorphic except at $s=1$. Along the way we obtain a new proof of Manin's conjecture on the asymptotic growth of points on $X^K(\\mathbb{Q})$ of boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04277","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"}