{"paper":{"title":"Irreducibility of generalized Hermite-Laguerre polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shanta Laishram, T. N. Shorey","submitted_at":"2013-06-04T12:32:22Z","abstract_excerpt":"For a rational $q=u+\\frac{\\alpha}{d}$ with $u, \\alpha, d\\in \\ACOBZ$ with $u\\ge 0, 1\\le \\alpha<d$, $\\gcd(\\alpha, d)=1$, the \\emph{generalized Hermite-Laguerre polynomials $G_q(x)$} are defined by \\begin{align*} G_q(x)&=a_nx^n+a_{n-1}(\\alpha +(n-1+u)d)x^{n-1}+\\cdots\\\\ &\\quad+a_1\\left(\\prod^{n-1}_{i=1}(\\alpha +(i+u)d)\\right)x+a_0 \\left(\\prod^{n-1}_{i=0}(\\alpha +(i+u)d)\\right) \\end{align*} where $a_0, a_1, \\cdots, a_n$ are arbitrary integers. We prove some irreducibility results of $G_q(x)$ when $q\\in \\{\\frac{1}{3}, \\frac{2}{3}\\}$ and extend some of the earlier irreducibility results when $q$ of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0745","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"}