{"paper":{"title":"Fixed point proportions for Galois groups of non-geometric iterated extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jamie Juul","submitted_at":"2016-03-19T15:22:35Z","abstract_excerpt":"Given a map $\\varphi:\\mathbb{P}^1\\rightarrow \\mathbb{P}^1$ of degree greater than 1 defined over a number field $k$, one can define a map $\\varphi_\\mathfrak{p}:\\mathbb{P}^1(\\mathfrak{o}_k/\\mathfrak{p})\\rightarrow \\mathbb{P}^1(\\mathfrak{o}_k/\\mathfrak{p})$ for each prime $\\mathfrak{p}$ of good reduction, induced by reduction modulo $\\mathfrak{p}$. It has been shown that for a typical $\\varphi$ the proportion of periodic points of $\\varphi_\\mathfrak{p}$ should tend to $0$ as $|\\mathbb{P}^1(\\mathfrak{o}_k/\\mathfrak{p})|$ grows. In this paper, we extend previous results to include a weaker set of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06103","kind":"arxiv","version":4},"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"}