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A note on ternary cyclotomic polynomials

Bin Zhang
대한수학회 (The Korean Mathematical Society)|2014.08|대한수학회보 (Bulletin of the KMS)|제51권 제4호|pp. 949-955

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참고문헌

키워드

cyclotomic polynomialternary cyclotomic polynomialcoefficients of cyclotomic polynomial
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초록

Let Φn(x) = P∑(n) k=0 a(n, k)xk denote the n-th cyclotomic polynomial. In this note, let p < q < r be odd primes, where q ≠ 1 (mod p) and r ≡ −2 (mod pq), we construct an explicit k such that a(pqr, k) = −2.

Abstract

Let Φn(x) = P∑(n) k=0 a(n, k)xk denote the n-th cyclotomic polynomial. In this note, let p < q < r be odd primes, where q ≠ 1 (mod p) and r ≡ −2 (mod pq), we construct an explicit k such that a(pqr, k) = −2.

참고문헌 (14)

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  10. H. W. Lenstra, "Vanishing sums of roots of unity, in: Proceedings, Bicentennial Congress Wiskundig Genootschap (Vrije Univ., Amsterdam, 1978), Part II", Math. Centre Tracts, 101, pp.249~268 (1978), Math. Centrum
  11. H. M¨oller, "¨Uber die Koeffizienten des n-ten Kreisteilungspolynoms", Math. Z, 119, pp.33~40 (1971)
  12. P. Moree, "Inverse cyclotomic polynomials", J. Number Theory, 129(3), pp.667~680 (2009)
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  14. J. Zhao, "Coefficients of ternary cyclotomic polynomials", J. Number Theory, 130(10), pp.2223~2237 (2010)

관련 논문AI추천

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