Defining polynomial of the first layer of anti-cyclotomic $\mathbf {Z}_3$-extension of imaginary quadratic fields of class number 1

Defining polynomial of the first layer of anti-cyclotomic $\mathbf {Z}_3$-extension of imaginary quadratic fields of class number 1

Jae Moon Kim and Jangheon Oh

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 80, Number 3 (2004), 18-19.

Abstract

In this paper, we explicitly compute defining polynomials of the first layer of anti-cyclotomic $\mathbf{Z}_3$-extension of imaginary quadratic fields of class number 1.

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Primary Subjects: 11R23, 11R32

Keywords: Iwasawa theory; anti-cyclotomic $\mathbf {Z}_3$-extension; Kummer extension; defining polynomial

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442135
Mathematical Reviews number (MathSciNet): MR2046261
Zentralblatt MATH identifier: 1050.11093
Digital Object Identifier: doi:10.3792/pjaa.80.18

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References

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Mathematical Reviews (MathSciNet): MR1728313

Zentralblatt MATH: 0977.11056

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Mathematical Reviews (MathSciNet): MR1801672

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Mathematical Reviews (MathSciNet): MR718674

Zentralblatt MATH: 0484.12001

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