Coefficients of cyclotomic polynomials

2009/09/05 by Pingzhi Yuan, Yuan, Pingzhi · 1 citation
Mathematics · #11B83 #11C08 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0909.0995

openalex publication_date 2009/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a(n, k) be the k-th coefficient of the n-th cyclotomic polynomial. Recently, Ji, Li and Moree \citeJLM09 proved that for any integer m≥1, \a(mn, k)| n, k∈ℕ\=ℤ. In this paper, we improve this result and prove that for any integers s>t≥0, \a(ns+t, k)| n, k∈ℕ\=ℤ.

Citations

• The Midterm Coefficient of the Cyclotomic Polynomial F pq (x)

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• Divisibility criteria and coefficient formulas for cyclotomic polynomials

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