{"paper":{"title":"Small zeros of quadratic forms outside of a union of varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Glenn Henshaw, Lenny Fukshansky, Wai Kiu Chan","submitted_at":"2013-07-02T00:21:20Z","abstract_excerpt":"Let $F$ be a quadratic form in $N \\geq 2$ variables defined on a vector space $V \\subseteq K^N$ over a global field $K$, and $\\Z \\subseteq K^N$ be a finite union of varieties defined by families of homogeneous polynomials over $K$. We show that if $V \\setminus \\Z$ contains a nontrivial zero of $F$, then there exists a linearly independent collection of small-height zeros of $F$ in $V\\setminus \\Z$, where the height bound does not depend on the height of $\\Z$, only on the degrees of its defining polynomials. As a corollary of this result, we show that there exists a small-height maximal totally "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0564","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"}