대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제55권5호
  • /
  • Pages.1491-1501
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  • 2018
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON CERTAIN MULTIPLES OF LITTLEWOOD AND NEWMAN POLYNOMIALS

  • 투고 : 2017.10.03
  • 심사 : 2018.05.02
  • 발행 : 2018.09.30
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초록

Polynomials with all the coefficients in {0, 1} and constant term 1 are called Newman polynomials, whereas polynomials with all the coefficients in {-1, 1} are called Littlewood polynomials. By exploiting an algorithm developed earlier, we determine the set of Littlewood polynomials of degree at most 12 which divide Newman polynomials. Moreover, we show that every Newman quadrinomial $X^a+X^b+X^c+1$, 15 > a > b > c > 0, has a Littlewood multiple of smallest possible degree which can be as large as 32765.

키워드

과제정보

연구 과제번호 : Number Systems, Spectra and Rational Fractal Tiles

연구 과제 주관 기관 : Research Council of Lithuania, FWF

참고문헌

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