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

Takashi FUKUDA; Keiichi KOMATSU

doi:10.3836/tjm/1244208291

Translator Disclaimer

June 2005 On the Iwasawa $\lambda$-Invariant of the Cyclotomic $\mathbf{Z}_2$-Extension of a Real Quadratic Field

Takashi FUKUDA, Keiichi KOMATSU

Tokyo J. Math. 28(1): 259-264 (June 2005). DOI: 10.3836/tjm/1244208291

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.

Citation

Download Citation

Takashi FUKUDA. Keiichi KOMATSU. "On the Iwasawa $\lambda$-Invariant of the Cyclotomic $\mathbf{Z}_2$-Extension of a Real Quadratic Field." Tokyo J. Math. 28 (1) 259 - 264, June 2005. https://doi.org/10.3836/tjm/1244208291