Document Type

Article

Publication Date

7-2007

Publication Title

Proceedings of the American Mathematical Society

Abstract

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.

Volume

135

Issue

7

First Page

1959

Last Page

1967

DOI

https://doi.org/10.1090/S0002-9939-07-08629-7

ISSN

0002-9939

Comments

First published in Proceedings of the American Mathematical Society 135 (July 2007), published by the American Mathematical Society. © 2007 American Mathematical Society.

Rights

© 2007 American Mathematical Society.

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