Construction of Zp -extensions with prescribed Iwasawa λ-invariants

Satoshi Fujii, Yoshihiro Ohgi, Manabu Ozaki

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

It is a basic problem in Iwasawa theory that the existence of a Zp-extension with prescribed Iwasawa invariants. Since the Iwasawa λ-invariant is regarded as an analogue of (twice of) the genus of an algebraic curve, we are especially interested in the problem on the Iwasawa λ-invariants. In this article, for a few prime numbers p, we show that there is a Zp-extension with prescribed Iwasawa λ-invariant by using Kida's formula, which is a number field analogue of the Riemann-Hurwitz formula.

Original languageEnglish
Pages (from-to)200-207
Number of pages8
JournalJournal of Number Theory
Volume118
Issue number2
DOIs
Publication statusPublished - 2006 Jun
Externally publishedYes

Fingerprint

Iwasawa Invariants
Iwasawa Theory
Analogue
Algebraic curve
Prime number
Number field
Genus

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Construction of Zp -extensions with prescribed Iwasawa λ-invariants. / Fujii, Satoshi; Ohgi, Yoshihiro; Ozaki, Manabu.

In: Journal of Number Theory, Vol. 118, No. 2, 06.2006, p. 200-207.

Research output: Contribution to journalArticle

Fujii, Satoshi ; Ohgi, Yoshihiro ; Ozaki, Manabu. / Construction of Zp -extensions with prescribed Iwasawa λ-invariants. In: Journal of Number Theory. 2006 ; Vol. 118, No. 2. pp. 200-207.
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