### Abstract

Let h_{n} denote the class number of Q(2 cos2π/2^{n}+2) which is a cyclic extension of degree 2^{n} over the rational number field Q. There are no known examples of h_{n} > 1. We prove that a prime number ℓ does not divide h_{n} for all n < 1 if ℓ is less than 10^{9} or ℓ satisfies a congruence relation ℓ ≢ ± 1 (mod 32).

Original language | English |
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Pages (from-to) | 1627-1635 |

Number of pages | 9 |

Journal | International Journal of Number Theory |

Volume | 7 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2011 Sep |

### Keywords

- Class number
- computation

### ASJC Scopus subject areas

- Algebra and Number Theory

## Fingerprint Dive into the research topics of 'Weber's class number problem in the cyclotomic Z<sub>2</sub>-extension of Q III'. Together they form a unique fingerprint.

## Cite this

Fukuda, T., & Komatsu, K. (2011). Weber's class number problem in the cyclotomic Z

_{2}-extension of Q III.*International Journal of Number Theory*,*7*(6), 1627-1635. https://doi.org/10.1142/S1793042111004782