{"paper":{"title":"A probabilistic approach to value sets of polynomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.PR"],"primary_cat":"math.CO","authors_text":"Qiang Wang, Zhicheng Gao","submitted_at":"2014-07-22T14:28:45Z","abstract_excerpt":"In this paper we study the distribution of the size of the value set for a random polynomial with degree at most $q-1$ over a finite field $\\mathbb{F}_q$. We obtain the exact probability distribution and show that the number of missing values tends to a normal distribution as $q$ goes to infinity. We obtain these results through a study of a random $r$-th order cyclotomic mappings. A variation on the size of the union of some random sets is also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5884","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"}