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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","authors_text":"Cheol-Min Park, Eunjeong Lee, Hoon Hong, Hyang-Sook Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-22T03:02:01Z","title":"Maximum Gap in (Inverse) Cyclotomic Polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4255","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7feccf94acde1a994813d76c3478eebea78a6233bb962933e405551916ad2189","target":"record","created_at":"2026-05-18T04:31:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ebfbd86bf25239e1b10c11923c98337d032ee459f7e7977190bb32e34e13abb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-22T03:02:01Z","title_canon_sha256":"9fc11e927b1de2d5e2ed8241827b3e085ee06330ea2b7688760d45e1e9c2801c"},"schema_version":"1.0","source":{"id":"1101.4255","kind":"arxiv","version":1}},"canonical_sha256":"698797299964b9d7e0dd84bd29644729db0b9880ab5b162eab846225fd44e34e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"698797299964b9d7e0dd84bd29644729db0b9880ab5b162eab846225fd44e34e","first_computed_at":"2026-05-18T04:31:11.256668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:11.256668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UzZYgRCznWwJ6SpVav8JvwnopNONVc8Lo2XM+5I38hy+yjHraYh7m9DHpsN+V8SBLDOQUaKK6C75ktlNJ0f+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:11.257145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7feccf94acde1a994813d76c3478eebea78a6233bb962933e405551916ad2189","sha256:1c36c2116a5a53eeb4ca260b54a262bc54035e4fd365438bce3d2742a8aa67ef"],"state_sha256":"a6b0d2b119f154dd1c26df7d1405d80932e447ebc083611efc051a2cd2d22143"}