Quintic polynomials of Hashimoto-Tsunogai, brumer and kummer

Masanari Kida; Guénaël Renault; Kazuhiro Yokoyama

doi:10.1142/s1793042109002250

Quintic polynomials of Hashimoto-Tsunogai, brumer and kummer

Masanari Kida
, Guénaël Renault
, Kazuhiro Yokoyama

University of Electro-Communications
INRIA Rocquencourt
Rikkyo University

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We establish an isomorphism between the quintic cyclic polynomials discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori. This enables us to solve the isomorphism problem for Hashimoto-Tsunogai polynomials and also Brumer's quintic polynomials.

langue originale	Anglais
Pages (de - à)	557-571
Nombre de pages	15
journal	International Journal of Number Theory
Volume	5
Numéro de publication	4
Les DOIs	https://doi.org/10.1142/s1793042109002250
état	Publié - 1 janv. 2009
Modification externe	Oui

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10.1142/s1793042109002250

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title = "Quintic polynomials of Hashimoto-Tsunogai, brumer and kummer",

abstract = "We establish an isomorphism between the quintic cyclic polynomials discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori. This enables us to solve the isomorphism problem for Hashimoto-Tsunogai polynomials and also Brumer's quintic polynomials.",

keywords = "Brumer's quintic polynomial, Cyclic quintic extension, Kummer theory, Quintic dihedral extension",

author = "Masanari Kida and Gu{\'e}na{\"e}l Renault and Kazuhiro Yokoyama",

year = "2009",

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T1 - Quintic polynomials of Hashimoto-Tsunogai, brumer and kummer

AU - Kida, Masanari

AU - Renault, Guénaël

AU - Yokoyama, Kazuhiro

PY - 2009/1/1

Y1 - 2009/1/1

N2 - We establish an isomorphism between the quintic cyclic polynomials discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori. This enables us to solve the isomorphism problem for Hashimoto-Tsunogai polynomials and also Brumer's quintic polynomials.

AB - We establish an isomorphism between the quintic cyclic polynomials discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori. This enables us to solve the isomorphism problem for Hashimoto-Tsunogai polynomials and also Brumer's quintic polynomials.

KW - Brumer's quintic polynomial

KW - Cyclic quintic extension

KW - Kummer theory

KW - Quintic dihedral extension

U2 - 10.1142/s1793042109002250

DO - 10.1142/s1793042109002250

M3 - Article

AN - SCOPUS:67649452510

SN - 1793-0421

VL - 5

SP - 557

EP - 571

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 4

ER -

Quintic polynomials of Hashimoto-Tsunogai, brumer and kummer

Résumé

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