{"paper":{"title":"On the Number of Dot Products Determined by a Large Set and One of its Translates in Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Giorgis Petridis","submitted_at":"2015-10-27T14:29:55Z","abstract_excerpt":"Let $E \\subseteq \\mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements, which satisfies $|E| > q$. There exist $x,y \\in E$ such that $|E \\cdot (y-x)| > q/2.$ In particular, $(E+E) \\cdot (E-E) = \\mathbb{F}_q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07918","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"}