{"paper":{"title":"On discrete values of bilinear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Iosevich, Misha Rudnev, Oliver Roche-Newton","submitted_at":"2015-12-08T21:51:08Z","abstract_excerpt":"This paper is an erratum to our paper, entitled \"On an application of Guth-Katz theorem\", Math. Res. Lett. 18 (2011), no. 4, 691-697.\n  Let $F$ be the real or complex field and $\\omega$ a non-degenerate skew-symmetric bilinear form in the plane $F^2$. We prove that for finite a point set $P\\subset F^2\\setminus\\{0\\}$, the set $T_\\omega(P)$ of nonzero values of $\\omega$ in $P\\times P$, if nonempty, has cardinality $\\Omega(N^{9/13}).$\n  A presumably near-sharp estimate $\\Omega(N/\\log N)$ was claimed in the abovemnetioned paper over the reals for a symmetric or skew-symmetric form $\\omega$. Howeve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02670","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"}