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

Ki Ichiro Hashimoto; Akinari Hoshi

doi:10.1090/S0025-5718-05-01750-3

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

Ki Ichiro Hashimoto^*, Akinari Hoshi

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

7 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 language	English
Pages (from-to)	1519-1530
Number of pages	12
Journal	Mathematics of Computation
Volume	74
Issue number	251
DOIs	https://doi.org/10.1090/S0025-5718-05-01750-3
Publication status	Published - 2005 Jul

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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10.1090/S0025-5718-05-01750-3

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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.",

keywords = "Cyclic polynomials, Cyclotomic numbers, Gaussian periods, Generic polynomials, Inverse Galois theory, Jacobi sums",

author = "Hashimoto, {Ki Ichiro} and Akinari Hoshi",

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

AU - Hashimoto, Ki Ichiro

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

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

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

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SN - 0025-5718

VL - 74

SP - 1519

EP - 1530

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 251

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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