{"paper":{"title":"On a generalization of Beiter Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bartlomiej Bzdega","submitted_at":"2014-07-12T07:54:44Z","abstract_excerpt":"We prove that for every $\\varepsilon>0$ and a nonnegative integer $\\omega$ there exist primes $p_1,p_2,\\ldots,p_\\omega$ such that for $n=p_1p_2\\ldots p_\\omega$ the height of the cyclotomic polynomial $\\Phi_n$ is at least $(1-\\varepsilon)c_\\omega M_n$, where $M_n=\\prod_{i=1}^{\\omega-2}p_i^{2^{\\omega-1-i}-1}$ and $c_\\omega$ is a constant depending only on $\\omega$; furthermore $\\lim_{\\omega\\to\\infty}c_\\omega^{2^{-\\omega}}\\approx0.71$. In our construction we can have $p_i>h(p_1p_2\\ldots p_{i-1})$ for all $i=1,2,\\ldots,\\omega$ and any function $h:\\mathbb{R}_+\\to\\mathbb{R}_+$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3359","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"}