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

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

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)

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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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