{"paper":{"title":"Wreath products and proportions of periodic points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jamie Juul, Kalyani Madhu, Par Kurlberg, Thomas J. Tucker","submitted_at":"2014-10-13T16:12:37Z","abstract_excerpt":"Let $\\varphi: {\\mathbb P}^1 \\longrightarrow {\\mathbb P}^1$ be a rational map of degree greater than one defined over a number field $k$. For each prime ${\\mathfrak p}$ of good reduction for $\\varphi$, we let $\\varphi_{\\mathfrak p}$ denote the reduction of $\\varphi$ modulo ${\\mathfrak p}$. A random map heuristic suggests that for large ${\\mathfrak p}$, the proportion of periodic points of $\\varphi_{\\mathfrak p}$ in ${\\mathbb P}^1({\\mathfrak o}_k/{\\mathfrak p})$ should be small. We show that this is indeed the case for many rational functions $\\varphi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3378","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"}