{"paper":{"title":"The set of stable primes for polynomial sequences with large Galois group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Ferraguti","submitted_at":"2017-04-07T12:26:55Z","abstract_excerpt":"Let $K$ be a number field with ring of integers $\\mathcal O_K$, and let $\\{f_k\\}_{k\\in \\mathbb N}\\subseteq \\mathcal O_K[x]$ be a sequence of monic polynomials such that for every $n\\in \\mathbb N$, the composition $f^{(n)}=f_1\\circ f_2\\circ\\ldots\\circ f_n$ is irreducible. In this paper we show that if the size of the Galois group of $f^{(n)}$ is large enough (in a precise sense) as a function of $n$, then the set of primes $\\mathfrak p\\subseteq\\mathcal O_K$ such that every $f^{(n)}$ is irreducible modulo $\\mathfrak p$ has density zero. Moreover, we prove that the subset of polynomial sequences "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02204","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"}