On the Iwasawa 𝜆-invariant of the cyclotomic ℤ₂-extension of ℚ(√𝕡)

Fukuda, Takashi; Komatsu, Keiichi

doi:10.1090/S0025-5718-09-02124-3

On the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb {Z}_2$-extension of $\mathbb {Q}(\sqrt {p} )$
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by Takashi Fukuda and Keiichi Komatsu;

Math. Comp. 78 (2009), 1797-1808

DOI: https://doi.org/10.1090/S0025-5718-09-02124-3

Published electronically: January 28, 2009

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Abstract:

We study the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb {Z}_2$-extension of $\mathbb {Q}(\sqrt {p} )$ for an odd prime number $p$ which satisfies $p\equiv 1\pmod {16}$ relating it to units having certain properties. We give an upper bound of $\lambda$ and show $\lambda =0$ in certain cases. We also give new numerical examples of $\lambda =0$.

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