{"paper":{"title":"Reciprocal cyclotomic polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pieter Moree","submitted_at":"2007-09-11T10:38:06Z","abstract_excerpt":"Let $\\Psi_n(x)$ be the monic polynomial having precisely all non-primitive $n$th roots of unity as its simple zeros. One has $\\Psi_n(x)=(x^n-1)/\\Phi_n(x)$, with $\\Phi_n(x)$ the $n$th cyclotomic polynomial. The coefficients of $\\Psi_n(x)$ are integers that like the coefficients of $\\Phi_n(x)$ tend to be surprisingly small in absolute value, e.g. for $n<561$ all coefficients of $\\Psi_n(x)$ are $\\le 1$ in absolute value. We establish various properties of the coefficients of $\\Psi_n(x)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1570","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"}