Ji, Chungang; Li, Weiping Values of coefficients of cyclotomic polynomials. (English) Zbl 1213.11059 Discrete Math. 308, No. 23, 5860-5863 (2008). Summary: Let \(a(k,n)\) be the \(k\)-th coefficient of the \(n\)-th cyclotomic polynomials. In 1987 [Proc. Japan Acad., Ser. A 63, 279–280 (1987; Zbl 0641.10008)], J. Suzuki proved that \(\{a(k,n)\mid n,\,k\in \mathbb N\}=\mathbb Z\). In this paper, we improve this result and prove that for any prime \(p\) and any integer \(l\geq 1\), we have \(\{a(k,p^ln)\mid n,\,k\in \mathbb N\} = \mathbb Z\).Part II, cf. the authors and P. Moree, Discrete Math. 309, No. 6, 1720–1723 (2009; Zbl 1221.11067) Cited in 1 ReviewCited in 3 Documents MSC: 11C08 Polynomials in number theory 11B83 Special sequences and polynomials Keywords:cyclotomic polynomials; Dirichlet’s theorem; arithmetic progressions Citations:Zbl 0641.10008; Zbl 1221.11067 PDFBibTeX XMLCite \textit{C. Ji} and \textit{W. Li}, Discrete Math. 308, No. 23, 5860--5863 (2008; Zbl 1213.11059) Full Text: DOI Online Encyclopedia of Integer Sequences: Consider the coefficients in the expansion of the n-th cyclotomic polynomial. a(n) is the difference between the extremes. References: [1] Bachman, G., Flat cyclotomic polynomials of order three, Bull. London Math. Soc., 38, 53-60 (2006) · Zbl 1178.11022 [2] Bachman, G., Ternary cyclotomic polynomials with an optimally large set of coefficients, Proc. Amer. Math. Soc., 132, 1943-1950 (2004) · Zbl 1050.11027 [3] Lenstra Jr., H. W., Vanishing sums of roots of unity, (Proc. Bicentennial Cong. Wiskundig Genootschap (1978), Vrije Univ.: Vrije Univ. Amsterdam), 249-268 [4] Migotti, A., Zur Theorie der Kreisteilungsgleichung, Sitzber. Math.-Naturwiss. Classe der Kaiser. Akad. der Wiss., 87, 7-14 (1883) · JFM 14.0127.01 [5] P. Moree, H. Hommersom, Value distribution of Ramanujan sums and of cyclotomic polynomial coefficients. arXiv: math.NT/0307352; P. Moree, H. Hommersom, Value distribution of Ramanujan sums and of cyclotomic polynomial coefficients. arXiv: math.NT/0307352 · Zbl 1313.11112 [6] Suzuki, J., On coefficients of cyclotomic polynomials, Proc. Japan Acad. Ser. A Math. Sci., 63, 279-280 (1987) · Zbl 0641.10008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.