{"paper":{"title":"On preperiodic points of rational functions defined over $\\mathbb{F}_p(t)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Jung Kyu Canci, Laura Paladino","submitted_at":"2016-01-27T09:06:53Z","abstract_excerpt":"Let $P\\in\\mathbb{P}_1(\\mathbb{Q})$ be a periodic point for a monic polynomial with coefficients in $\\mathbb{Z}$. With elementary techniques one sees that the minimal periodicity of $P$ is at most $2$. Recently we proved a generalization of this fact to the set of all rational functions defined over ${\\mathbb{Q}}$ with good reduction everywhere (i.e. at any finite place of $\\mathbb{Q}$). The set of monic polynomials with coefficients in $\\mathbb{Z}$ can be characterized, up to conjugation by elements in PGL$_2({\\mathbb{Z}})$, as the set of all rational functions defined over $\\mathbb{Q}$ with a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07293","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"}