{"paper":{"title":"Maximum Gap in (Inverse) Cyclotomic Polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cheol-Min Park, Eunjeong Lee, Hoon Hong, Hyang-Sook Lee","submitted_at":"2011-01-22T03:02:01Z","abstract_excerpt":"Let $g(f)$ denote the maximum of the differences (gaps) between two consecutive exponents occurring in a polynomial $f$. Let $\\Phi_n$ denote the $n$-th cyclotomic polynomial and let $\\Psi_n$ denote the $n$-th inverse cyclotomic polynomial. In this note, we study $g(\\Phi_n)$ and $g(\\Psi_n)$ where $n$ is a product of odd primes, say $p_1 < p_2 < p_3$, etc. It is trivial to determine $g(\\Phi_{p_1})$, $g(\\Psi_{p_1})$ and $g(\\Psi_{p_1p_2})$. Hence the simplest non-trivial cases are $g(\\Phi_{p_1p_2})$ and $g(\\Psi_{p_1p_2p_3})$. We provide an exact expression for $g(\\Phi_{p_1p_2}).$ We also provide a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4255","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"}