Weber's class number problem in the cyclotomic Z2-extension of Q III

Takashi Fukuda; Keiichi Komatsu

doi:10.1142/S1793042111004782

Weber's class number problem in the cyclotomic Z₂-extension of Q III

Takashi Fukuda, Keiichi Komatsu

研究成果: Article › 査読

15 被引用数 (Scopus)

抄録

Let h_n denote the class number of Q(2 cos2π/2ⁿ+2) which is a cyclic extension of degree 2ⁿ over the rational number field Q. There are no known examples of h_n > 1. We prove that a prime number ℓ does not divide h_n for all n < 1 if ℓ is less than 10⁹ or ℓ satisfies a congruence relation ℓ ≢ ± 1 (mod 32).

本文言語	English
ページ（範囲）	1627-1635
ページ数	9
ジャーナル	International Journal of Number Theory
巻	7
号	6
DOI	https://doi.org/10.1142/S1793042111004782
出版ステータス	Published - 2011 9

ASJC Scopus subject areas

Algebra and Number Theory

文献へのアクセス

10.1142/S1793042111004782

他のファイルとリンク

フィンガープリント「Weber's class number problem in the cyclotomic Z<sub>2</sub>-extension of Q III」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル

@article{0476105882cb4899900606e7105f3f09,

title = "Weber's class number problem in the cyclotomic Z2-extension of Q III",

abstract = "Let hn denote the class number of Q(2 cos2π/2n+2) which is a cyclic extension of degree 2n over the rational number field Q. There are no known examples of hn > 1. We prove that a prime number ℓ does not divide hn for all n < 1 if ℓ is less than 109 or ℓ satisfies a congruence relation ℓ ≢ ± 1 (mod 32).",

keywords = "Class number, computation",

author = "Takashi Fukuda and Keiichi Komatsu",

year = "2011",

month = sep,

doi = "10.1142/S1793042111004782",

language = "English",

volume = "7",

pages = "1627--1635",

journal = "International Journal of Number Theory",

issn = "1793-0421",

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

number = "6",

}

TY - JOUR

T1 - Weber's class number problem in the cyclotomic Z2-extension of Q III

AU - Fukuda, Takashi

AU - Komatsu, Keiichi

PY - 2011/9

Y1 - 2011/9

N2 - Let hn denote the class number of Q(2 cos2π/2n+2) which is a cyclic extension of degree 2n over the rational number field Q. There are no known examples of hn > 1. We prove that a prime number ℓ does not divide hn for all n < 1 if ℓ is less than 109 or ℓ satisfies a congruence relation ℓ ≢ ± 1 (mod 32).

AB - Let hn denote the class number of Q(2 cos2π/2n+2) which is a cyclic extension of degree 2n over the rational number field Q. There are no known examples of hn > 1. We prove that a prime number ℓ does not divide hn for all n < 1 if ℓ is less than 109 or ℓ satisfies a congruence relation ℓ ≢ ± 1 (mod 32).

KW - Class number

KW - computation

UR - http://www.scopus.com/inward/record.url?scp=80052587043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052587043&partnerID=8YFLogxK

U2 - 10.1142/S1793042111004782

DO - 10.1142/S1793042111004782

M3 - Article

AN - SCOPUS:80052587043

VL - 7

SP - 1627

EP - 1635

JO - International Journal of Number Theory

JF - International Journal of Number Theory

SN - 1793-0421

IS - 6

ER -