Proceedings of the American Mathematical Society
For each prime power pm, we realize the classical cyclotomic polynomial Φpm(x) as one of a collection of 3m different polynomials in Z[x]. We show that the new polynomials are similar to Φpm(x) in many ways, including that their discriminants all have the form ±pc. We show also that the new polynomials are more complicated than Φpm(x) in other ways, including that their complex roots are generally fractal in appearance.
© 2007 American Mathematical Society.
David P. Roberts. Fractalized cyclotomic polynomials. Proceedings of the American Mathematical Society 135 (2007), no. 7, 1959-1967.