{"paper":{"title":"On the value set of small families of polynomials over a finite field, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Guillermo Matera, Mariana P\\'erez, Melina Privitelli","submitted_at":"2013-10-11T21:04:58Z","abstract_excerpt":"We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients a_{d-1},...,a_{d-s} are fixed. Our estimate asserts that \\mathcal{V}(d,s,\\bfs{a})=\\mu_d\\,q+\\mathcal{O}(q^{1/2}), where \\mathcal{V}(d,s,\\bfs{a}) is such an average cardinality, \\mu_d:=\\sum_{r=1}^d{(-1)^{r-1}}/{r!} and \\bfs{a}:=(a_{d-1},...,a_{d-s}). We also prove that \\mathcal{V}_2(d,s,\\bfs{a})=\\mu_d^2\\,q^2+\\mathcal{O}(q^{3/2}), where that \\mathcal{V}_2(d,s,\\bfs{a}) is the average second moment on any family of monic polynomials of Fq[T] "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3293","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"}