{"paper":{"title":"On the sums of any k points in finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.CO","authors_text":"David Covert, Doowon Koh, Youngjin Pi","submitted_at":"2014-03-24T20:22:33Z","abstract_excerpt":"For a set $E\\subset \\mathbb F_q^d$, we define the $k$-resultant magnitude set as $ \\Delta_k(E) =\\{\\|\\textbf{x}_1 + \\dots + \\textbf{x}_k\\|\\in \\mathbb F_q: \\textbf{x}_1, \\dots, \\textbf{x}_k \\in E\\},$ where $\\|\\textbf{v}\\|=v_1^2+\\cdots+ v_d^2$ for $\\textbf{v}=(v_1, \\ldots, v_d) \\in \\mathbb F_q^d.$ In this paper we find a connection between a lower bound of the cardinality of the $k$-resultant magnitude set and the restriction theorem for spheres in finite fields. As a consequence, it is shown that if $E\\subset \\mathbb F_q^d$ with $|E|\\geq C q^{\\frac{d+1}{2}-\\frac{1}{6d+2}},$ then $|\\Delta_3(E)|\\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6138","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"}