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

Takashi Fukuda; Keiichi Komatsu

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

Takashi Fukuda^*, Keiichi Komatsu

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

Let h_n denote the class number of ℚ(2cos(27π/2 ⁿ⁺²)). Weber proved that h_n is odd for all n ≥ 1. We claim that if I is a prime number less than 10⁷, then for all n≥ 1, ℓ does not divide h_n.

Original language	English
Pages (from-to)	213-222
Number of pages	10
Journal	Experimental Mathematics
Volume	18
Issue number	2
Publication status	Published - 2009

Keywords

Class number
Computation

ASJC Scopus subject areas

Mathematics(all)

Cite this

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

abstract = "Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.",

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author = "Takashi Fukuda and Keiichi Komatsu",

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volume = "18",

pages = "213--222",

journal = "Experimental Mathematics",

issn = "1058-6458",

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

AU - Fukuda, Takashi

AU - Komatsu, Keiichi

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N2 - Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.

AB - Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.

KW - Class number

KW - Computation

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M3 - Article

AN - SCOPUS:68949110186

SN - 1058-6458

VL - 18

SP - 213

EP - 222

JO - Experimental Mathematics

JF - Experimental Mathematics

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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