### Abstract

Let K_{n} be the n-th layer of the cyclotomic Z2-extension of Q( √ 5) and h_{n} the class number of K_{n}. We prove that, if ℓ is a prime number less than 6 104, then ℓ does not divide h_{n} for any non-negative integer n.

Original language | English |
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Pages (from-to) | 69-81 |

Number of pages | 13 |

Journal | Tokyo Journal of Mathematics |

Volume | 39 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 Jun 1 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{2}-extension of Q(√5).

*Tokyo Journal of Mathematics*,

*39*(1), 69-81. https://doi.org/10.3836/tjm/1459367258

**A Class Number Problem for the Cyclotomic Z _{2}-extension of Q(√5).** / Aoki, Takuya.

Research output: Contribution to journal › Article

_{2}-extension of Q(√5)',

*Tokyo Journal of Mathematics*, vol. 39, no. 1, pp. 69-81. https://doi.org/10.3836/tjm/1459367258

_{2}-extension of Q(√5). Tokyo Journal of Mathematics. 2016 Jun 1;39(1):69-81. https://doi.org/10.3836/tjm/1459367258

}

TY - JOUR

T1 - A Class Number Problem for the Cyclotomic Z2-extension of Q(√5)

AU - Aoki, Takuya

PY - 2016/6/1

Y1 - 2016/6/1

N2 - Let Kn be the n-th layer of the cyclotomic Z2-extension of Q( √ 5) and hn the class number of Kn. We prove that, if ℓ is a prime number less than 6 104, then ℓ does not divide hn for any non-negative integer n.

AB - Let Kn be the n-th layer of the cyclotomic Z2-extension of Q( √ 5) and hn the class number of Kn. We prove that, if ℓ is a prime number less than 6 104, then ℓ does not divide hn for any non-negative integer n.

UR - http://www.scopus.com/inward/record.url?scp=84983657076&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983657076&partnerID=8YFLogxK

U2 - 10.3836/tjm/1459367258

DO - 10.3836/tjm/1459367258

M3 - Article

AN - SCOPUS:84983657076

VL - 39

SP - 69

EP - 81

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 1

ER -