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

^*この研究の対応する著者

研究成果: Article › 査読

16 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月

ASJC Scopus subject areas

代数と数論

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10.1142/S1793042111004782

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引用スタイル

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