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The height of a class of ternary cyclotomic polynomials

Bin Zhang
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회보 (Bulletin of the KMS)|제54권 제1호|pp. 43-50

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참고문헌

키워드

coefficientheight of a cyclotomic polynomialternary cyclotomic polynomial
주제분류수학

초록

Let $A(n)$ denote the largest absolute value of the coefficients of $n$-th cyclotomic polynomial $\Phi_n(x)$ and let $p<q<r$ be odd primes. In this note, we give an infinite family of cyclotomic polynomials $\Phi_{pqr}(x)$ with $A(pqr)=3$, without fixing $p$.

Abstract

Let $A(n)$ denote the largest absolute value of the coefficients of $n$-th cyclotomic polynomial $\Phi_n(x)$ and let $p<q<r$ be odd primes. In this note, we give an infinite family of cyclotomic polynomials $\Phi_{pqr}(x)$ with $A(pqr)=3$, without fixing $p$.

참고문헌 (17)

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  2. G. Bachman, "On a class of ternary inclusion-exclusion polynomials", Integers, 11(A8), pp.1~14 (2011)
  3. M. Beiter, "Magnitude of the coefficients of the cyclotomic polynomial Fpqr. II", Duke Math. J, 38, pp.591~594 (1971)
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  10. C. G. Ji, "A special family of cyclotomic polynomials of order three", Science China Math, 53, pp.2269~2274 (2010)
  11. N. Kaplan, "Flat cyclotomic polynomials of order three", J. Number Theory, 127(1), pp.118~126 (2007)
  12. T. Y. Lam, "On the cyclotomic polynomial Φ p q(X)", Amer. Math. Monthly, 103(7), pp.562~564 (1996)
  13. H. M¨oller, "¨Uber die Koeffizienten des n-ten Kreisteilungspolynoms", Math. Z, 119, pp.33~40 (1971)
  14. R. Thangadurai, "Cyclotomic Fields and Related Topics, Pune, 1999", pp.311~322 (2000), Bhaskaracharya Pratishthana
  15. Bin Zhang, "A note on ternary cyclotomic polynomials", 대한수학회보, 51(4), pp.949~955 (2014), 대한수학회
  16. Bin Zhang, "ON A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALS", 대한수학회보, 52(6), pp.1911~1924 (2015), 대한수학회
  17. J. Zhao, "Coefficients of ternary cyclotomic polynomials", J. Number Theory, 130(10), pp.2223~2237 (2010)

관련 논문AI추천

A note on ternary cyclotomic polynomialsBin Zhang대한수학회 · 대한수학회보2014 · 제51권 제4호ON A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALSBin Zhang, Yu Zhou대한수학회 · 대한수학회보2015 · 제52권 제6호CYCLOTOMIC POLYNOMIALS OVER CYCLOTOMIC FIELDS김성두, 이준복대한수학회 · 대한수학회논문집2012 · 제27권 제3호Modified cyclotomic polynomials이기석, Ae-Kyoung Cha, Miyeon Kwon, Seong-Mo Yang대한수학회 · 대한수학회보2022 · 제59권 제6호On the irreducibility of sum of two reciprocal polynomialsDoYong Kwon, Minsang Bang대한수학회 · 대한수학회보2016 · 제53권 제3호The $p$-part of divisor class numbers for cyclotomic function fieldsDaisuke Shiomi대한수학회 · 대한수학회논문집2023 · 제38권 제3호

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