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The Height of a Family of Ternary Cyclotomic Polynomials(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2022年01期
Page:
12-16
Research Field:
·数学·
Publishing date:

Info

Title:
The Height of a Family of Ternary Cyclotomic Polynomials
Author(s):
Zhang Bin1; Sun Wenyu2; Du Jinzhengnan1; Bi Xinyu1
(1.School of Mathematical Sciences,Qufu Normal University,Qufu 273165,China)(2.School of Mathematics and Quantitative Economics,Shandong University of Finance and Economics,Jinan 250014,China)
Keywords:
cyclotomic polynomial; ternary cyclotomic polynomial; the height of cyclotomic polynomial
PACS:
O156.2
DOI:
10.3969/j.issn.1001-4616.2022.01.003
Abstract:
Let A(n)denote the largest absolute value of the coefficients of the n-th cyclotomic polynomial Φn(x). In this paper, for odd primes 5<q<r with r≡±3(mod 5q),we show that 2≤A(5qr)≤3.

References:

[1] KAPLAN N. Flat cyclotomic polynomials of order three[J]. Journal of number theory,2007,127:118-126.
[2]黄立君. 三阶分圆多项式的系数[D]. 南京:南京师范大学,2012.
[3]ELDER S. Flat cyclotomic polynomials:a new approach[J]. arXiv:1207.5811,2012.
[4]ZHANG B. The height of a class of ternary cyclotomic polynomials[J]. Bulletin of the Korean Mathematic Society,2017,54:43-50.
[5]ZHAO J,ZHANG X K. Coefficients of ternary cyclotomic polynomials[J]. Journal of number theory,2010,130:2223-2237.
[6]LAM T Y,LEUNG K H. On the cyclotomic polynomial Φpq(X)[J]. American mathematical monthly,1996,103:562-564.

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