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

Ki Ichiro 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 1

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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