On the 2-part of the class numbers of cyclotomic fields of prime power conductors

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概要

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• Let p be an odd prime number and ℓ a prime number with ℓ ≠ p. Let Kn = Q(ζpn+1) be the pn+1-st cyclotomic field. Let hn and hn- be the class number and the relative class number of Kn, respectively. When ℓ = 2, we give an explicit bound mp depending on p such that the ratio hn-/hn-1- is odd for all n > mp. When ℓ ≥ 3, we also give a corresponding result on the ℓ-part of the relative class number of Kn+(ζℓ). As an application, we show that when p ≤ 509, the ratio hn/h0 is odd for all n ≥ 1.

• Mathematical Society of Japanの論文
• 2012-01-01

著者

• Ichimura Humio

  Faculty of Science, Ibaraki University

• Ichimura Humio

  Faculty Of Science Ibaraki University

• Nakajima Shoichi

  Department Of Mathematics Gakushuin University

関連論文

• Hilbert-Speiser number fields and the complex conjugation
• Hilbert-Speiser number fields and the complex conjugation
• On the 2-part of the class numbers of cyclotomic fields of prime power conductors
• Stickelberger ideals of conductor p and their application

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