A capitulation problem and Greenberg's conjecture on real quadratic fields

T. Fukuda; Keiichi Komatsu

doi:10.1090/S0025-5718-96-00676-X

A capitulation problem and Greenberg's conjecture on real quadratic fields

T. Fukuda^*, Keiichi Komatsu

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

We give a sufficient condition in order that an ideal of a real quadratic field F capitulates in the cyclotomic ℤ₃-extension of F by using a unit of an intermediate field. Moreover, we give new examples of F's for which Greenberg's conjecture holds by calculating units of fields of degree 6, 18, 54 and 162.

Original language	English
Pages (from-to)	313-318
Number of pages	6
Journal	Mathematics of Computation
Volume	65
Issue number	213
DOIs	https://doi.org/10.1090/S0025-5718-96-00676-X
Publication status	Published - 1996 Jan
Externally published	Yes

Keywords

Computation
Iwasawa invariants
Real quadratic fields unit groups

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics
Computational Mathematics

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10.1090/S0025-5718-96-00676-X

Cite this

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abstract = "We give a sufficient condition in order that an ideal of a real quadratic field F capitulates in the cyclotomic ℤ3-extension of F by using a unit of an intermediate field. Moreover, we give new examples of F's for which Greenberg's conjecture holds by calculating units of fields of degree 6, 18, 54 and 162.",

keywords = "Computation, Iwasawa invariants, Real quadratic fields unit groups",

author = "T. Fukuda and Keiichi Komatsu",

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AB - We give a sufficient condition in order that an ideal of a real quadratic field F capitulates in the cyclotomic ℤ3-extension of F by using a unit of an intermediate field. Moreover, we give new examples of F's for which Greenberg's conjecture holds by calculating units of fields of degree 6, 18, 54 and 162.

KW - Computation

KW - Iwasawa invariants

KW - Real quadratic fields unit groups

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ER -

A capitulation problem and Greenberg's conjecture on real quadratic fields

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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