Tokyo Journal of Mathematics

On the Iwasawa Invariants of the Cyclotomic $\mathbb{Z}_{2}$-Extensions of Certain Real Quadratic Fields

Yoshinori Nishino

Full-text: Open access

Abstract

We study some conditions that the Iwasawa $\lambda$-, $\mu$-invariants of the the cyclotomic $\mathbb{Z}_{2}$-extension of $k = \mathbb{Q}(\sqrt{pq})$ with $p \equiv 7 \pmod{8}, q \equiv 1 \pmod{8}, (\frac{p}{q}) = -1$ are zero.

Article information

Source
Tokyo J. Math., Volume 29, Number 1 (2006), 239-245.

Dates
First available in Project Euclid: 20 December 2006

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1166661877

Digital Object Identifier
doi:10.3836/tjm/1166661877

Mathematical Reviews number (MathSciNet)
MR2258282

Zentralblatt MATH identifier
1170.11039

Citation

Nishino, Yoshinori. On the Iwasawa Invariants of the Cyclotomic $\mathbb{Z}_{2}$-Extensions of Certain Real Quadratic Fields. Tokyo J. Math. 29 (2006), no. 1, 239--245. doi:10.3836/tjm/1166661877. https://projecteuclid.org/euclid.tjm/1166661877


Export citation

References

  • T. Fukuda and K. Komatsu, On the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbbZ_2$-extension of a real quadratic field, to appear in Tokyo J., Math.
  • R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math., 98 (1976) 263–284.
  • H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag (1952).
  • K. Iwasawa, On $\Gamma$-extension of algebraic number fields, Bull. Amer. Math. Soc., 65 (1959), 183–226.
  • K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 257–258.
  • S. Kuroda, Über den Dirichletschen Körper, J. Fac. Sci. Imp. Univ. Tokyo Sec. I., 4 (1943), 383–406.
  • M. Ozaki and H. Taya, On the Iwasawa $\lambda_2$-invariants of certain families of real quadratic fields, Manuscripta Math., 94 (1997), 437–444.
  • L. Rédei and H. Reichardt, Die Anzahl der durch 4 teilbaren Invarianten der Klassengruppe eines beliebigen quadratischen Zahlkörpers, J. Reine. Angew. Math., 170 (1933), 69–74.
  • L. C. Washington, Introduction to Cyclotomic Fields (2nd. Edition), GTM 83, Springer (1997).