{"paper":{"title":"Incidence bounds and applications over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Claudiu Valculescu, Le Anh Vinh, Nguyen Duy Phuong, Nguyen Minh Sang, Thang Pham","submitted_at":"2016-01-03T13:01:55Z","abstract_excerpt":"In this paper we introduce a unified approach to deal with incidence problems between points and varieties over finite fields. More precisely, we prove that the number of incidences $I(\\mathcal{P}, \\mathcal{V})$ between a set $\\mathcal{P}$ of points and a set $\\mathcal{V}$ of varieties of a certain form satisfies $$\\left\\vert I(\\mathcal{P},\\mathcal{V})-\\frac{|\\mathcal{P}||\\mathcal{V}|}{q^k}\\right\\vert\\le q^{dk/2}\\sqrt{|\\mathcal{P}||\\mathcal{V}|}.$$\n  This result is a generalization of the results of Vinh (2011), Bennett et al. (2014), and Cilleruelo et al. (2015). As applications of our incide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00290","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"}