{"paper":{"title":"The power-saving Manin-Peyre's conjectures for a senary cubic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kevin Destagnol, Sandro Bettin","submitted_at":"2018-05-07T21:39:12Z","abstract_excerpt":"Using recent work of the first author~\\cite{Bet}, we prove a strong version of the Manin-Peyre's conjectures with a full asymptotic and a power-saving error term for the two varieties respectively in $\\mathbb{P}^2 \\times \\mathbb{P}^2$ with bihomogeneous coordinates $[x_1:x_2:x_3],[y_1:y_2,y_3]$ and in $\\mathbb{P}^1\\times \\mathbb{P}^1 \\times \\mathbb{P}^1$ with multihomogeneous coordinates $[x_1:y_1],[x_2:y_2],[x_3:y_3]$ defined by the same equation $x_1y_2y_3+x_2y_1y_3+x_3y_1y_2=0$. We thus improve on recent work of Blomer, Br\\\"udern and Salberger \\cite{BBS} and provide a different proof based "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02756","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"}