{"paper":{"title":"Distribution of reducible polynomials with a given coefficient set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shane Chern","submitted_at":"2016-02-24T08:34:42Z","abstract_excerpt":"For a given set of integers $\\mathcal{S}$, let $\\mathcal{R}_n^*(\\mathcal{S})$ denote the set of reducible polynomials $f(X)=a_nX^n+a_{n-1}X^{n-1}+\\cdots+a_1X+a_0$ over $\\mathbb{Z}[X]$ with $a_i\\in\\mathcal{S}$ and $a_0a_n\\ne 0$. In this note, we shall give an explicit bound of $|\\mathcal{R}_n^*(\\mathcal{S})|$. We also present an application of this bound to reducible bivariate polynomials over $\\mathbb{Z}[X,Y]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07431","kind":"arxiv","version":3},"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"}