Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations

Kiichiro Hashimoto, Akinari Hoshi

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    A general method of constructing families of cyclic polynomials over ℚ with more than one parameter will be discussed, which may be called a geometric generalization of the Gaussian period relations. Using this, we obtain explicit multi-parametric families of cyclic polynomials over ℚ of degree 3 ≤ e ≤ 7. We also give a simple family of cyclic polynomials with one parameter in each case, by specializing our parameters.

    Original languageEnglish
    Pages (from-to)1519-1530
    Number of pages12
    JournalMathematics of Computation
    Volume74
    Issue number251
    DOIs
    Publication statusPublished - 2005 Jul

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    Polynomials
    Polynomial
    Family
    Generalization

    Keywords

    • Cyclic polynomials
    • Cyclotomic numbers
    • Gaussian periods
    • Generic polynomials
    • Inverse Galois theory
    • Jacobi sums

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Applied Mathematics
    • Computational Mathematics

    Cite this

    Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations. / Hashimoto, Kiichiro; Hoshi, Akinari.

    In: Mathematics of Computation, Vol. 74, No. 251, 07.2005, p. 1519-1530.

    Research output: Contribution to journalArticle

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