{"paper":{"title":"On the value set of small families of polynomials over a finite field, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Eda Cesaratto, Guillermo Matera, Mariana P\\'erez, Melina Privitelli","submitted_at":"2013-06-07T15:12:17Z","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 holds without restrictions on the characteristic of Fq and asserts that V(d,s,\\bfs{a})=\\mu_d.q+\\mathcal{O}(1), where 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},.., d_{d-s}). We provide an explicit upper bound for the constant underlying the \\mathcal{O}--notation in terms of d and s with \"good\" behavior. Our approach reduces the que"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1744","kind":"arxiv","version":3},"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"}