{"paper":{"title":"M\\\"obius-Frobenius maps on irreducible polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniela Oliveira, F.E. Brochero Mart\\'inez, Lucas Reis","submitted_at":"2018-12-21T00:26:00Z","abstract_excerpt":"Let $n$ be a positive integer and let $\\mathbb F_{q^n}$ be the finite field with $q^n$ elements, where $q$ is a power of a prime. This paper introduces a natural action of the Projective Semilinear Group $\\text{P}\\Gamma \\text{L}(2, q^n)=\\text{PGL}(2, q^n)\\rtimes \\text{Gal}(\\mathbb{F}_{q^n}/\\mathbb{F}_q)$ on the set of monic irreducible polynomials over the finite field $\\mathbb{F}_{q^n}$. Our main results provide information on the characterization and number of fixed points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08900","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"}