{"paper":{"title":"Polynomial Values in Subfields and Affine Subspaces of Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Igor Shparlinski, Oliver Roche-Newton","submitted_at":"2014-07-08T20:58:46Z","abstract_excerpt":"For an integer $r$, a prime power $q$, and a polynomial $f$ over a finite field ${\\mathbb F}_{q^r}$ of $q^r$ elements, we obtain an upper bound on the frequency of elements in an orbit generated by iterations of $f$ which fall in a proper subfield of ${\\mathbb F}_{q^r}$. We also obtain similar results for elements in affine subspaces of ${\\mathbb F}_{q^r}$, considered as a linear space over ${\\mathbb F}_q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2273","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"}