Browse > Article
http://dx.doi.org/10.4134/BKMS.b150339

THE HEIGHT OF A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALS  

Zhang, Bin (School of Mathematical Sciences Qufu Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 43-50 More about this Journal
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.
Keywords
height of a cyclotomic polynomial; ternary cyclotomic polynomial; coefficient;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 G. Bachman, Flat cyclotomic polynomials of order three, Bull. London Math. Soc. 38 (2006), no. 1, 53-60.   DOI
2 G. Bachman and P. Moree, On a class of ternary inclusion-exclusion polynomials, Integers 11 (2011), A8, 1-14.   DOI
3 M. Beiter, Magnitude of the coefficients of the cyclotomic polynomial $F_{pqr}$. II, Duke Math. J. 38 (1971), 591-594.   DOI
4 M. Beiter, Coefficients of the cyclotomic polynomial $F_{3qr}$(x), Fibonacci Quart. 16 (1978), no. 4, 302-306.
5 D. M. Bloom, On the coefficients of the cyclotomic polynomials, Amer. Math. Monthly 75 (1968), 372-377.   DOI
6 D. Broadhurst, Flat ternary cyclotomic polynomials, http://tech.groups.yahoo.com/group/primenumbers/message/20305(2009).
7 S. Elder, Flat cyclotomic polynomials: a new approach, arXiv:1207.5811v1, 2012.
8 T. J. Flanagan, On the coefficients of ternary cyclotomic polynomials, MS Thesis, University of Nevada Las Vegas, 2006.
9 Y. Gallot, P. Moree, and R. Wilms, The family of ternary cyclotomic polynomials with one free prime, Involve 4 (2011), no. 4, 317-341.   DOI
10 C. G. Ji, A special family of cyclotomic polynomials of order three, Science China Math. 53 (2010), 2269-2274.   DOI
11 N. Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), no. 1, 118-126.   DOI
12 T. Y. Lam and K. H. Leung, On the cyclotomic polynomial ${\Phi}_{pq}$(X), Amer. Math. Monthly 103 (1996), no. 7, 562-564.   DOI
13 H. Moller, Uber die Koeffizienten des n-ten Kreisteilungspolynoms, Math. Z. 119 (1971), 33-40.   DOI
14 R. Thangadurai, On the coefficients of cyclotomic polynomials, in: Cyclotomic Fields and Related Topics, Pune, 1999, 311-322, Bhaskaracharya Pratishthana, Pune, 2000.
15 B. Zhang, A note on ternary cyclotomic polynomials, Bull. KoreanMath. Soc. 51 (2014), no. 4, 949-955.   DOI
16 B. Zhang and Y. Zhou, On a class of ternary cyclotomic polynomials, Bull. Korean Math. Soc. 52 (2015), no. 6, 1911-1924.   DOI
17 J. Zhao and X. K. Zhang, Coefficients of ternary cyclotomic polynomials, J. Number Theory 130 (2010), no. 10, 2223-2237.   DOI