ON A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALS

Title & Authors
ON A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALS
ZHANG, BIN; ZHOU, YU;

Abstract
A cyclotomic polynomial $\small{{\Phi}_n(x)}$ is said to be ternary if n
Keywords
ternary cyclotomic polynomial;flat cyclotomic polynomial;coefficient of cyclotomic polynomial;
Language
English
Cited by
1.
Remarks on the flatness of ternary cyclotomic polynomials, International Journal of Number Theory, 2017, 13, 02, 529
References
1.
A. Arnold and M. Monagan, Data on the heights and lengths of cyclotomic polynomials, Available: http://oldweb.cecm.sfu.ca/-ada26/cyclotomic/data.html.

2.
G. Bachman, Flat cyclotomic polynomials of order three, Bull. London Math. Soc. 38 (2006), no. 1, 53-60.

3.
G. Bachman and P. Moree, On a class of ternary inclusion-exclusion polynomials, Integers 11 (2011), 1-14.

4.
A. S. Bang, Om Lingingen \${\Phi}_n\$(x) = 0, Tidsskr. Math. 6 (1895), 6-12.

5.
M. Beiter, Coefficients of the cyclotomic polynomial \$F_{3qr}\$(x), Fibonacci Quart. 16 (1978), no. 4, 302-306.

6.
D. M. Bloom, On the coefficients of the cyclotomic polynomials, Amer. Math. Monthly 75 (1968), 372-377.

7.

8.
B. Bzdega, Jumps of ternary cyclotomic coefficients, Acta Arith. 163 (2014), no. 3, 203-213.

9.
C. Cobeli, Y. Gallot, P. Moree, and A. Zaharescu, Sister Beiter and Kloosterman: A tale of cyclotomic coefficients and modular inverses, Indag. Math. (N.S.) 24 (2013), no. 4, 915-929.

10.
D. Duda, The maximal coefficient of ternary cyclotomic polynomials with one free prime, Int. J. Number Theory 10 (2014), no. 4, 1067-1080.

11.
S. Elder, Flat cyclotomic polynomials: A new approach, arXiv:1207.5811v1, 2012.

12.
T. Flanagan, On the coefficients of ternary cyclotomic polynomials, MS Thesis, University of Nevada Las Vegas, 2006.

13.
Y. Gallot and P. Moree, Ternary cyclotomic polynomials having a large coefficient, J. Reine Angew. Math. 632 (2009), 105-125.

14.
Y. Gallot, P. Moree, and R. Wilms, The family of ternary cyclotomic polynomials with one free prime, Involve 4 (2011), no. 4, 317-341.

15.
H. Hong, E. Lee, H. S. Lee, and C. M. Park, Maximum gap in (inverse) cyclotomic polynomial, J. Number Theory 132 (2012), no. 10, 2297-2315.

16.
C. G. Ji, A special family of cyclotomic polynomials of order three, Sci. China Math. 53 (2010), no. 9, 2269-2274.

17.
N. Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), no. 1, 118-126.

18.
T. Y. Lam and K. H. Leung, On the cyclotomic polynomial \${\Phi}_{pq}\$(X), Amer. Math. Monthly 103 (1996), no. 7, 562-564.

19.
E. Lehmer, On the magnitude of the coefficients of the cyclotomic polynomials, Bull. Amer. Math. Soc. 42 (1936), no. 6, 389-392.

20.
H. Moller, Uber die Koeffizienten des n-ten Kreisteilungspolynoms, Math. Z. 119 (1971), 33-40.

21.
P. Moree and E. Rosu, Non-Beiter ternary cyclotomic polynomials with an optimally large set of coefficients, Int. J. Number Theory 8 (2012), no. 8, 1883-1902.

22.
R. Thangadurai, On the coefficients of cyclotomic polynomials, In: Cyclotomic fields and related topics (Pune, 1999), 311-322, Bhaskaracharya Pratishthana, Pune, 2000.

23.
B. Zhang, A note on ternary cyclotomic polynomials, Bull. Korean Math. Soc. 51 (2014), no. 4, 949-955.

24.
J. Zhao and X. K. Zhang, Coefficients of ternary cyclotomic polynomials, J. Number Theory 130 (2010), no. 10, 2223-2237.