The class group of zp-extensions over totally real number fields

Manabu Ozaki

doi:10.2748/tmj/1178225114

The class group of z_p-extensions over totally real number fields

Manabu Ozaki

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Let p be an odd prime. We shall give a criterion for p-divisibility of the class number of the w-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 andπ-invariants of it to vanish.

Original language	English
Pages (from-to)	431-435
Number of pages	5
Journal	Tohoku Mathematical Journal
Volume	49
Issue number	3
DOIs	https://doi.org/10.2748/tmj/1178225114
Publication status	Published - 1997 Jan 1

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2748/tmj/1178225114

Cite this

@article{54c3299cc50240edbff6f0f36128792c,

title = "The class group of zp-extensions over totally real number fields",

abstract = "Let p be an odd prime. We shall give a criterion for p-divisibility of the class number of the w-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 andπ-invariants of it to vanish.",

author = "Manabu Ozaki",

year = "1997",

month = jan,

day = "1",

doi = "10.2748/tmj/1178225114",

language = "English",

volume = "49",

pages = "431--435",

journal = "Tohoku Mathematical Journal",

issn = "0040-8735",

publisher = "Tohoku University, Mathematical Institute",

number = "3",

}

TY - JOUR

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

AU - Ozaki, Manabu

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Let p be an odd prime. We shall give a criterion for p-divisibility of the class number of the w-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 andπ-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 w-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 andπ-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

U2 - 10.2748/tmj/1178225114

DO - 10.2748/tmj/1178225114

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 -

The class group of z_p-extensions over totally real number fields

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this