### Abstract

Let h_{n} denote the class number of ℚ(2cos(27π/2 ^{n+2})). Weber proved that h_{n} is odd for all n ≥ 1. We claim that if I is a prime number less than 10^{7}, then for all n≥ 1, ℓ does not divide h_{n}.

Original language | English |
---|---|

Pages (from-to) | 213-222 |

Number of pages | 10 |

Journal | Experimental Mathematics |

Volume | 18 |

Issue number | 2 |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Class number
- Computation

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{2}-extension of ℚ.

*Experimental Mathematics*,

*18*(2), 213-222.

**Weber's class number problem in the cyclotomic ℤ _{2}-extension of ℚ.** / Fukuda, Takashi; Komatsu, Keiichi.

Research output: Contribution to journal › Article

_{2}-extension of ℚ',

*Experimental Mathematics*, vol. 18, no. 2, pp. 213-222.

_{2}-extension of ℚ. Experimental Mathematics. 2009;18(2):213-222.

}

TY - JOUR

T1 - Weber's class number problem in the cyclotomic ℤ2-extension of ℚ

AU - Fukuda, Takashi

AU - Komatsu, Keiichi

PY - 2009

Y1 - 2009

N2 - Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.

AB - Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.

KW - Class number

KW - Computation

UR - http://www.scopus.com/inward/record.url?scp=68949110186&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68949110186&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:68949110186

VL - 18

SP - 213

EP - 222

JO - Experimental Mathematics

JF - Experimental Mathematics

SN - 1058-6458

IS - 2

ER -