International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 38, Pages 2447-2453
Total characters and Chebyshev polynomials
Division of Natural Sciences, New College of Florida, 5700 NorthTamiami Trail, Sarasota 34243, FL, USA
Received 8 January 2002
Copyright © 2003 Eirini Poimenidou and Homer Wolfe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The total character of a finite group is defined as the sum of all the irreducible characters of . K. W. Johnson asks when it is possible to express as a polynomial with integer coefficients in a single irreducible character. In this paper, we give a complete answer to Johnson's question for all
finite dihedral groups. In particular, we show that, when such a polynomial exists, it is unique and it is the sum of certain Chebyshev polynomials of the first kind in any faithful irreducible character of the dihedral group .