{"paper":{"title":"The $k$-resultant modulus set problem on algebraic varieties over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"David Covert, Doowon Koh, Youngjin Pi","submitted_at":"2015-08-11T19:00:02Z","abstract_excerpt":"We study the $k$-resultant modulus set problem in the $d$-dimensional vector space $\\mathbb F_q^d$ over the finite field $\\mathbb F_q$ with $q$ elements. Given $E\\subset \\mathbb F_q^d$ and an integer $k\\ge 2$, the $k$-resultant modulus set, denoted by $\\Delta_k(E)$, is defined as $$ \\Delta_k(E)=\\{\\|x^1\\pm x^2 \\pm \\cdots \\pm x^k\\|\\in \\mathbb F_q: x^j\\in E, ~j=1,2,\\ldots, k\\},$$ where $\\|\\alpha\\|=\\alpha_1^2+\\cdots+ \\alpha_d^2$ for $\\alpha=(\\alpha_1, \\ldots, \\alpha_d) \\in \\mathbb F_q^d.$ In this setting, the $k$-resultant modulus set problem is to determine the minimal cardinality of $E\\subset \\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02688","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"}