[1]张 彬,孙雯宇,杜金征南,等.一类三阶分圆多项式的高度[J].南京师大学报(自然科学版),2022,(01):12-16.[doi:10.3969/j.issn.1001-4616.2022.01.003]
 Zhang Bin,Sun Wenyu,Du Jinzhengnan,et al.The Height of a Family of Ternary Cyclotomic Polynomials[J].Journal of Nanjing Normal University(Natural Science Edition),2022,(01):12-16.[doi:10.3969/j.issn.1001-4616.2022.01.003]
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一类三阶分圆多项式的高度()
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《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

卷:
期数:
2022年01期
页码:
12-16
栏目:
·数学·
出版日期:
2022-03-15

文章信息/Info

Title:
The Height of a Family of Ternary Cyclotomic Polynomials
文章编号:
1001-4616(2022)01-0012-05
作者:
张 彬1孙雯宇2杜金征南1毕昕宇1
(1.曲阜师范大学数学科学学院,山东 曲阜 273165)(2.山东财经大学数学与数量经济学院,山东 济南 250014)
Author(s):
Zhang Bin1Sun Wenyu2Du Jinzhengnan1Bi 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)
关键词:
分圆多项式三阶分圆多项式分圆多项式的高度
Keywords:
cyclotomic polynomialternary cyclotomic polynomialthe height of cyclotomic polynomial
分类号:
O156.2
DOI:
10.3969/j.issn.1001-4616.2022.01.003
文献标志码:
A
摘要:
A(n)表示n次分圆多项式的所有系数绝对值的最大值. 本文在5<q<r为素数且满足r≡&#177;3(mod 5q)的条件下,证明了2≤A(5qr)≤3.
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.

参考文献/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.

备注/Memo

备注/Memo:
收稿日期:2021-09-24.
基金项目:国家自然科学基金项目(11801303)、山东省自然科学基金项目(ZR2019QA016)、中国博士后科学基金面上一等资助项目(2018M640617).
通讯作者:张彬,博士,副教授,研究方向:代数数论. E-mail:zhangb2015@qfnu.edu.cn
更新日期/Last Update: 1900-01-01