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December 2009 A Class Number Problem in the Cyclotomic $\mathbf{Z}_3$-extension of $\mathbb{Q}$
Tokyo J. Math. 32(2): 549-558 (December 2009). DOI: 10.3836/tjm/1264170249


Let $\Omega_n$ be the $n$-th layer of the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}$ and $h_n$ the class number of $\Omega_n$. We claim that if $\ell$ is a prime number less than $10^4$, then $\ell$ does not divide $h_n$ for any positive integer $n$.


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Takayuki MORISAWA. "A Class Number Problem in the Cyclotomic $\mathbf{Z}_3$-extension of $\mathbb{Q}$." Tokyo J. Math. 32 (2) 549 - 558, December 2009.


Published: December 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1205.11116
MathSciNet: MR2589962
Digital Object Identifier: 10.3836/tjm/1264170249

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

Vol.32 • No. 2 • December 2009
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