### Abstract

Let p be an odd prime. We shall give a criterion for p-divisibility of the class number of the n-th layer of a Z_{p}-extension over a certain totally real number field by means of the value of the p-adic zeta function. We shall also discuss the capitulation in such a Z_{p}-extension and a sufficient condition for the Iwasawa λ-and μ-invariants of it to vanish.

Original language | English |
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Pages (from-to) | 431-435 |

Number of pages | 5 |

Journal | Tohoku Mathematical Journal |

Volume | 49 |

Issue number | 3 |

Publication status | Published - 1997 Sep |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{p}-extensions over totally real number fields.

*Tohoku Mathematical Journal*,

*49*(3), 431-435.

**The class group of Z _{p}-extensions over totally real number fields.** / Ozaki, Manabu.

Research output: Contribution to journal › Article

_{p}-extensions over totally real number fields',

*Tohoku Mathematical Journal*, vol. 49, no. 3, pp. 431-435.

_{p}-extensions over totally real number fields. Tohoku Mathematical Journal. 1997 Sep;49(3):431-435.

}

TY - JOUR

T1 - The class group of Zp-extensions over totally real number fields

AU - Ozaki, Manabu

PY - 1997/9

Y1 - 1997/9

N2 - Let p be an odd prime. We shall give a criterion for p-divisibility of the class number of the n-th layer of a Zp-extension over a certain totally real number field by means of the value of the p-adic zeta function. We shall also discuss the capitulation in such a Zp-extension and a sufficient condition for the Iwasawa λ-and μ-invariants of it to vanish.

AB - Let p be an odd prime. We shall give a criterion for p-divisibility of the class number of the n-th layer of a Zp-extension over a certain totally real number field by means of the value of the p-adic zeta function. We shall also discuss the capitulation in such a Zp-extension and a sufficient condition for the Iwasawa λ-and μ-invariants of it to vanish.

UR - http://www.scopus.com/inward/record.url?scp=0031285634&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031285634&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031285634

VL - 49

SP - 431

EP - 435

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

SN - 0040-8735

IS - 3

ER -