Classifying brumer's quintic polynomials by weak mordellweil groups

Masanari Kida; Yuichi Rikuna; Atsushi Sato

doi:10.1142/S1793042110003162

Classifying brumer's quintic polynomials by weak mordellweil groups

Masanari Kida, Yuichi Rikuna, Atsushi Sato

SCI - Mathematics

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

4 Citations (Scopus)

Abstract

We develop a general classification theory for Brumer's dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.

Original language	English
Pages (from-to)	691-704
Number of pages	14
Journal	International Journal of Number Theory
Volume	6
Issue number	3
DOIs	https://doi.org/10.1142/S1793042110003162
Publication status	Published - 2010 May

Keywords

Brumer's quintic polynomial
Dihedral extension
Elliptic curve
Kummer theory

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S1793042110003162

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title = "Classifying brumer's quintic polynomials by weak mordellweil groups",

abstract = "We develop a general classification theory for Brumer's dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.",

keywords = "Brumer's quintic polynomial, Dihedral extension, Elliptic curve, Kummer theory",

author = "Masanari Kida and Yuichi Rikuna and Atsushi Sato",

note = "Funding Information: This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) No. 19340011, (C) No. 18540048, (C) No. 19540015, and (C) No. 19540057.",

year = "2010",

month = may,

doi = "10.1142/S1793042110003162",

language = "English",

volume = "6",

pages = "691--704",

journal = "International Journal of Number Theory",

issn = "1793-0421",

publisher = "World Scientific Publishing Co. Pte Ltd",

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T1 - Classifying brumer's quintic polynomials by weak mordellweil groups

AU - Kida, Masanari

AU - Rikuna, Yuichi

AU - Sato, Atsushi

N1 - Funding Information: This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) No. 19340011, (C) No. 18540048, (C) No. 19540015, and (C) No. 19540057.

PY - 2010/5

Y1 - 2010/5

N2 - We develop a general classification theory for Brumer's dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.

AB - We develop a general classification theory for Brumer's dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.

KW - Brumer's quintic polynomial

KW - Dihedral extension

KW - Elliptic curve

KW - Kummer theory

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DO - 10.1142/S1793042110003162

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JO - International Journal of Number Theory

JF - International Journal of Number Theory

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ER -

Classifying brumer's quintic polynomials by weak mordellweil groups

Abstract

Keywords

ASJC Scopus subject areas

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