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

^*Corresponding author for this work

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

17 Citations (Scopus)

Abstract

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).

Original language	English
Pages (from-to)	1627-1635
Number of pages	9
Journal	International Journal of Number Theory
Volume	7
Issue number	6
DOIs	https://doi.org/10.1142/S1793042111004782
Publication status	Published - 2011 Sept

Keywords

Class number
computation

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1142/S1793042111004782

Cite this

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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).",

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