Fractalized cyclotomic polynomials

David P. Roberts

    Research output: Contribution to journalArticlepeer-review

    1 Scopus citations

    Abstract

    For each prime power pm, we realize the classical cyclotomic polynomial Φpm(x) as one of a collection of 3 m 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.

    Original languageEnglish (US)
    Pages (from-to)1959-1967
    Number of pages9
    JournalProceedings of the American Mathematical Society
    Volume135
    Issue number7
    DOIs
    StatePublished - Jul 2007

    Keywords

    • Cyclotomic polynomial
    • Discriminant
    • Fractal
    • Galois

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