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2009 Weber's Class Number Problem in the Cyclotomic $\Z_2$-Extension of $\Q$
Takashi Fukuda, Keiichi Komatsu
Experiment. Math. 18(2): 213-222 (2009).

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 $h_n$.

Citation

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Takashi Fukuda. Keiichi Komatsu. "Weber's Class Number Problem in the Cyclotomic $\Z_2$-Extension of $\Q$." Experiment. Math. 18 (2) 213 - 222, 2009.

Information

Published: 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1189.11033
MathSciNet: MR2549691

Subjects:
Primary: 11G15, 11R27, 11Y40

Rights: Copyright © 2009 A K Peters, Ltd.

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Vol.18 • No. 2 • 2009
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