Hostname: page-component-7d8f8d645b-xs5cw Total loading time: 0 Render date: 2023-05-28T10:52:23.992Z Has data issue: false Feature Flags: { "useRatesEcommerce": true } hasContentIssue false

Resultants of Chebyshev Polynomials: the First, Second, Third, and Fourth Kinds

Published online by Cambridge University Press:  20 November 2018

Masakazu Yamagishi*
Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan. e-mail:
Rights & Permissions[Opens in a new window]


HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give an explicit formula for the resultant of Chebyshev polynomials of the first, second, third, and fourth kinds. We also compute the resultant of modified cyclotomic polynomials.

Research Article
Copyright © Canadian Mathematical Society 2015


[1] Apostol, T. M., Resultants ofcydotomic polynomials. Proc. Amer. Math. Soc. 24 (1970), 457462. http://dx.doi.Org/10.1090/S0002–9939-1970-0251010-X CrossRefGoogle Scholar
[2] Diederichsen, F.-E., Ùber die Ausreduktion ganzzahliger Gruppendarstellungen bei arithmetischer Âquivalenz. Abh. Math. Sem. Hansischen Univ. 13 (1940), 357412. http://dx.doi.Org/10.1007/BF02940768 CrossRefGoogle Scholar
[3] Dresden, G., Resultants of cydotomic polynomials. Rocky Mountain J. Math. 42 (2012), no. 5, 14611469.–42-5-1461 CrossRefGoogle Scholar
[4] Jacobs, D. P., Rayes, M. O., and Trevisan, V., The resultant of Chebyshev polynomials. Canad. Math. Bull. 54 (2011), no. 2, 288296. http://dx.doi.Org/10.4153/CMB-2011–013-1 CrossRefGoogle Scholar
[5] Lehmer, E. T., A numerical function applied to cydotomy. Bull. Amer. Math. Soc. 36 (1930), no. 4, 291298. http://dx.doi.Org/10.1090/S0002-9904-1930-04939-3 CrossRefGoogle Scholar
[6] Lemmermeyer, F., Reciprocity laws. From Euler to Eisenstein. Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2000.Google Scholar
[7] Louboutin, S., Resultants of cydotomic polynomials. Publ. Math. Debrecen 50 (1997), no. 12, 7577.Google Scholar
[8] Lemmermeyer, F., Resultants of Chebyshev polynomials: a short proof. Canad. Math. Bull. 56 (2013), no. 3, 602605.–002-1 Google Scholar
[9] Liineburg, H., Resultanten von Kreisteilungspolynomen. Arch. Math. (Basel) 42 (1984), no. 2, 139144. http://dx.doi.Org/10.1007/BF01772933 CrossRefGoogle Scholar
[10] McKay, J. H. and S, S. S.. Wang, A chain rule for the resultant of two polynomials. Arch. Math. (Basel) 53 (1989), no. 4, 347351. http://dx.doi.Org/10.1007/BF01195214 CrossRefGoogle Scholar
[11] Mason, J. C. and Handscomb, D. C., Chebyshev polynomials. Chapman & Hall/CRC, Boca Raton, FL, 2003.Google Scholar
[12] Rivlin, T. J., Chebyshev polynomials. From approximation theory to algebra and number theory. Second éd., Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1990.Google Scholar
[13] Yamagishi, M., A note on Chebyshev polynomials, cydotomic polynomials and twin primes. J. Number Theory 133 (2013), no. 7, 24552463. http://dx.doi.Org/10.1016/j.jnt.2O13.01.008 CrossRefGoogle Scholar