Tokyo Journal of Mathematics

On the Iwasawa $\lambda$-Invariant of the Cyclotomic $\mathbf{Z}_2$-Extension of a Real Quadratic Field

Takashi FUKUDA and Keiichi KOMATSU

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Abstract

We study the $\lambda$-invariant of the cyclotomic $\mathbf{Z}_2$-extension of $\mathbf{Q}(\sqrt{pq})$ with $p\equiv 3\pmod{8}$, $q\equiv 1\pmod{8}$ and $\bigl(\frac{q}{p}\bigr)=-1$. With further conditions on $q$, we show that $\lambda$-invariant is zero.

Article information

Source
Tokyo J. Math., Volume 28, Number 1 (2005), 259-264.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208291

Digital Object Identifier
doi:10.3836/tjm/1244208291

Mathematical Reviews number (MathSciNet)
MR2149635

Zentralblatt MATH identifier
1080.11080

Subjects
Primary: 11R23: Iwasawa theory

Citation

FUKUDA, Takashi; KOMATSU, Keiichi. On the Iwasawa $\lambda$-Invariant of the Cyclotomic $\mathbf{Z}_2$-Extension of a Real Quadratic Field. Tokyo J. Math. 28 (2005), no. 1, 259--264. doi:10.3836/tjm/1244208291. https://projecteuclid.org/euclid.tjm/1244208291


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References

  • T. Fukuda, K. Komatsu, M. Ozaki and H. Taya, On Iwasawa $\lambda_p$-invariants of relative real cyclic extensions of degree $p$, Tokyo J. Math. 20-2 (1997), 475–480.
  • K. Iwasawa, Riemann-Hurwitz formula and $p$-adic Galois representation for number fields, Tohoku Math. J. 33 (1981), 263–288.
  • M. Ozaki and H. Taya, On the Iwasawa $\lambda_2$-invariants of certain family of real quadratic fields, Manuscripta Math. 94 (1997), 437–444.
  • L. C. Washington, Introduction to Cyclotomic Fields, 2nd edition, Graduate Texts in Math., 83, Springer-Verlag, New York, Heidelberg, Berlin (1997).