Experimental Mathematics

Weber's Class Number Problem in the Cyclotomic $\Z_2$-Extension of $\Q$

Takashi Fukuda and Keiichi Komatsu

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Abstract

Let $h_n$ denote the class number of $\Q(2\cos(2\pi/2^{n+2}))$. Weber proved that $h_n$ is odd for all $n\geq 1$. We claim that if $\ell$ is a prime number less than $10^7$, then for all $n\geq 1$, $\ell$ does not divide $h_n$.

Article information

Source
Experiment. Math., Volume 18, Issue 2 (2009), 213-222.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.em/1259158432

Mathematical Reviews number (MathSciNet)
MR2549691

Zentralblatt MATH identifier
1189.11033

Subjects
Primary: 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22] 11R27: Units and factorization 11Y40: Algebraic number theory computations

Keywords
Class number computation

Citation

Fukuda, Takashi; Komatsu, Keiichi. Weber's Class Number Problem in the Cyclotomic $\Z_2$-Extension of $\Q$. Experiment. Math. 18 (2009), no. 2, 213--222. https://projecteuclid.org/euclid.em/1259158432


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