{"paper":{"title":"Discriminant and root separation of integral polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Dmitry Zaporozhets, Friedrich G\\\"otze","submitted_at":"2014-07-23T20:56:09Z","abstract_excerpt":"Consider a random polynomial $$ G_Q(x)=\\xi_{Q,n}x^n+\\xi_{Q,n-1}x^{n-1}+...+\\xi_{Q,0} $$ with independent coefficients uniformly distributed on $2Q+1$ integer points $\\{-Q, ..., Q\\}$. Denote by $D(G_Q)$ the discriminant of $G_Q$. We show that there exists a constant $C_n$, depending on $n$ only such that for all $Q\\ge 2$ the distribution of $D(G_Q)$ can be approximated as follows $$ \\sup_{-\\infty\\leq a\\leq b\\leq\\infty}|\\mathbb{P}(a\\leq \\frac{D(G_Q)}{Q^{2n-2}}\\leq b)-\\int_a^b\\varphi_n(x)\\, dx|\\leq\\frac{C_n}{\\log Q}, $$ where $\\varphi_n$ denotes the distribution function of the discriminant of a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6388","kind":"arxiv","version":2},"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"}