{"paper":{"title":"The generalized k-resultant modulus set problem in 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":"2017-03-02T04:18:43Z","abstract_excerpt":"Let $\\mathbb F_q^d$ be the $d$-dimensional vector space over the finite field $\\mathbb F_q$ with $q$ elements. Given $k$ sets $E_j\\subset \\mathbb F_q^d$ for $j=1,2,\\ldots, k$, the generalized $k$-resultant modulus set, denoted by $\\Delta_k(E_1,E_2, \\ldots, E_k)$, is defined by $$ \\Delta_k(E_1,E_2, \\ldots, E_k)=\\left\\{\\|{\\bf x}^1+{\\bf x}^2+\\cdots+{\\bf x}^k\\|\\in \\mathbb F_q:{\\bf x}^j\\in E_j,\\, j=1,2,\\ldots, k\\right\\},$$ where $\\|{\\bf y}\\|={\\bf y}_1^2+ \\cdots + {\\bf y}_d^2$ for ${\\bf y}=({\\bf y}_1, \\ldots, {\\bf y}_d)\\in \\mathbb F_q^d.$ We prove that if $\\prod\\limits_{j=1}^3 |E_j| \\ge C q^{3\\left("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00609","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"}