{"paper":{"title":"Solubility of a family of conics with polynomial coefficients in many variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mathieu Da Silva","submitted_at":"2025-11-25T13:10:37Z","abstract_excerpt":"We study the proportion of conics given by $(\\mathcal{C}_{\\mathbf{F}, \\mathbf{y}}) : F_0(\\mathbf{y})x_0^2 + F_1(\\mathbf{y})x_1^2 = F_2( \\mathbf{y})x_2^2 $ which have a rational point $\\mathbf{x} = (x_0 :x_1:x_2) \\in \\mathbb{P}^2(\\mathbb{Q})$, where $\\mathbf{y} = (y_0 : \\dots : y_n)\\in \\mathbb{P}^n(\\mathbb{Q})$ and $F_0,F_1,F_2 \\in \\mathbb{Z}[X_0,\\ldots, X_n]$ are homogeneous polynomials in many variables of the same degree $d$. We provide an asymptotic formula for the number of $\\mathbf{y}$ of bounded height such that the corresponding conic $(\\mathcal{C}_{\\mathbf{F}, \\mathbf{y}})$ has a ratio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.20282","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.20282/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}