대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권3호
  • /
  • Pages.449-454
  • /
  • 2012
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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CYCLOTOMIC POLYNOMIALS OVER CYCLOTOMIC FIELDS

  • 투고 : 2011.02.01
  • 발행 : 2012.07.31
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초록

In this paper, we find the minimal polynomial of a primitive root of unity over cyclotomic fields. From this, we factorize cyclotomic polynomials over cyclotomic fields and investigate the coefficients of ${\Phi}_{3n}(x)$ when 3∤$n$.

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참고문헌

  1. M. Beiter, Magnitude of the coefficients of the cyclotomic polynomial $F_{pqr}$, Amer. Math. Monthly 75 (1968), 370-372. https://doi.org/10.2307/2313416
  2. G. P. Dresden, On the middle coefficient of a cyclotomic polynomial, Amer. Math. Monthly 111 (2004), 531-533. https://doi.org/10.2307/4145075
  3. M.-C. Kang, Minimal polynomials over cyclotomic fields, Amer. Math. Monthly 104 (1997), no. 3, 258-260. https://doi.org/10.2307/2974793
  4. T. Y. Lam and K. H. Leung, On the cyclotomic polynomial ${\Phi}_{pq}$(X), Amer.Math. Monthly 103 (1996), no. 7, 562-564. https://doi.org/10.2307/2974668