{"paper":{"title":"Lower Bounds for Maximum Gap in (Inverse) Cyclotomic Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eunjeong Lee, Hoon Hong, Mary Ambrosino","submitted_at":"2017-02-24T16:30:55Z","abstract_excerpt":"The maximum gap $g(f)$ of a polynomial $f$ is the maximum of the differences (gaps) between two consecutive exponents that appear in $f$. Let $\\Phi_{n}$ and $\\Psi_{n}$ denote the $n$-th cyclotomic and $n$-th inverse cyclotomic polynomial, respectively. In this paper, we give several lower bounds for $g(\\Phi_{n})$ and $g(\\Psi_{n})$, where $n$ is the product of odd primes. We observe that they are very often exact. We also give an exact expression for $g(\\Psi_{n})$ under a certain condition. Finally we conjecture an exact expression for $g(\\Phi_{n})$ under a certain condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07650","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"}