{"paper":{"title":"Equidistribution of values of linear forms on a cubic hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sam Chow","submitted_at":"2015-04-29T12:48:14Z","abstract_excerpt":"Let $C$ be a cubic form with rational coefficients in $n$ variables, and let $h$ be the $h$-invariant of $C$. Let $L_1, \\ldots, L_r$ be linear forms with real coefficients such that if $\\boldsymbol{\\alpha} \\in \\mathbb{R}^r \\setminus \\{ \\boldsymbol{0} \\}$ then $\\boldsymbol{\\alpha} \\cdot \\mathbf{L}$ is not a rational form. Assume that $h > 16 + 8 r$. Let $\\boldsymbol{\\tau} \\in \\mathbb{R}^r$, and let $\\eta$ be a positive real number. We prove an asymptotic formula for the weighted number of integer solutions $\\mathbf{x} \\in [-P,P]^n$ to the system $C(\\mathbf{x}) = 0, \\: |\\mathbf{L}(\\mathbf{x}) - "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07837","kind":"arxiv","version":1},"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"}