The minimal polynomial of 2cos(pi/q) and Dickson polynomials

Bayad A., CANGÜL İ. N.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.13, pp.7014-7022, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 218 Issue: 13
  • Publication Date: 2012
  • Doi Number: 10.1016/j.amc.2011.12.044
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.7014-7022
  • Keywords: Hecke groups, Minimal polynomials, Cyclotomic polynomials, Chebychev polynomials, Dickson polynomials, Mobius inversion
  • Bursa Uludag University Affiliated: Yes


The number lambda(q) = 2cos(pi/q), q is an element of N, q >= 3, appears in the study of Hecke groups which are Fuchsian groups, and in the study of regular polyhedra. There are many partial results about the minimal polynomial of this algebraic number. Here we obtain the general formula and it is Mobius inversion for this minimal polynomial by means of the Dickson polynomials and the Mobius inversion theory. Moreover, we investigate the homogeneous cyclotomic, Chebychev and Dickson polynomials in two variables and we show that our main results in one variable case nicely extend to this situation. In this paper, the deep results concerning these polynomials are proved by elementary arguments. (C) 2011 Elsevier Inc. All rights reserved.