{"paper":{"title":"Polynomial maps on vector spaces over a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michiel Kosters","submitted_at":"2014-04-28T07:27:49Z","abstract_excerpt":"Let $l$ be a finite field of cardinality $q$ and let $n$ be in $\\mathbb{Z}_{\\geq 1}$. Let $f_1,\\ldots,f_n \\in l[x_1,\\ldots,x_n]$ not all constant and consider the evaluation map $f=(f_1,\\ldots,f_n) \\colon l^n \\to l^n$. Set $\\mathrm{deg}(f)=\\max_i \\mathrm{deg}(f_i)$. Assume that $l^n \\setminus f(l^n)$ is not empty. We will prove \\begin{align*}\n  |l^n\\setminus f(l^n)| \\geq \\frac{n(q-1)}{\\mathrm{deg}(f)}. \\end{align*} This improves previous known bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6884","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"}