International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 384016 | https://doi.org/10.1155/S0161171203201046

Eirini Poimenidou, Homer Wolfe, "Total characters and Chebyshev polynomials", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 384016, 7 pages, 2003. https://doi.org/10.1155/S0161171203201046

Total characters and Chebyshev polynomials

Received08 Jan 2002

Abstract

The total character τ of a finite group G is defined as the sum of all the irreducible characters of G. K. W. Johnson asks when it is possible to express τ 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 G.

Copyright © 2003 Hindawi Publishing Corporation. 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.


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