### 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 language | English |
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Pages (from-to) | 1519-1530 |

Number of pages | 12 |

Journal | Mathematics of Computation |

Volume | 74 |

Issue number | 251 |

DOIs | |

Publication status | Published - 2005 Jul |

### Fingerprint

### 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

*Mathematics of Computation*,

*74*(251), 1519-1530. https://doi.org/10.1090/S0025-5718-05-01750-3

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

Research output: Contribution to journal › Article

*Mathematics of Computation*, vol. 74, no. 251, pp. 1519-1530. https://doi.org/10.1090/S0025-5718-05-01750-3

}

TY - JOUR

T1 - Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations

AU - Hashimoto, Kiichiro

AU - Hoshi, Akinari

PY - 2005/7

Y1 - 2005/7

N2 - 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.

AB - 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.

KW - Cyclic polynomials

KW - Cyclotomic numbers

KW - Gaussian periods

KW - Generic polynomials

KW - Inverse Galois theory

KW - Jacobi sums

UR - http://www.scopus.com/inward/record.url?scp=21644482059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21644482059&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-05-01750-3

DO - 10.1090/S0025-5718-05-01750-3

M3 - Article

AN - SCOPUS:21644482059

VL - 74

SP - 1519

EP - 1530

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 251

ER -