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Fractalized Cyclotomic Polynomials, David P. Roberts

Mathematics Publications

For each prime power p^m, we realize the classical cyclotomic polynomial Φ_p^m(x) as one of a collection of 3^m different polynomials in Z[x]. We show that the new polynomials are similar to Φ_p^m(x) in many ways, including that their discriminants all have the form ±p^c. We show also that the new polynomials are more complicated than Φ_p^m(x) in other ways, including that their complex roots are generally fractal in appearance.