Tokyo Journal of Mathematics

A Class Number Problem for the Cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(\sqrt{5})$

Takuya AOKI

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Abstract

Let $K_n$ be the $n$-th layer of the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(\sqrt{5})$ and $h_n$ the class number of $K_n$. We prove that, if $\ell$ is a prime number less than $6\cdot10^4$, then $\ell$ does not divide $h_n$ for any non-negative integer $n$.

Article information

Source
Tokyo J. Math., Volume 39, Number 1 (2016), 69-81.

Dates
First available in Project Euclid: 30 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1459367258

Digital Object Identifier
doi:10.3836/tjm/1459367258

Mathematical Reviews number (MathSciNet)
MR3543132

Zentralblatt MATH identifier
06643264

Citation

AOKI, Takuya. A Class Number Problem for the Cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(\sqrt{5})$. Tokyo J. Math. 39 (2016), no. 1, 69--81. doi:10.3836/tjm/1459367258. https://projecteuclid.org/euclid.tjm/1459367258


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