Computation of ℤ₃-invariants of real quadratic fields

Taya, Hisao

doi:10.1090/S0025-5718-96-00721-1

Computation of $\mathbb {Z}_3$-invariants of real quadratic fields
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Math. Comp. 65 (1996), 779-784 Request permission

Abstract:

Let $k$ be a real quadratic field and $p$ an odd prime number which splits in $k$. In a previous work, the author gave a sufficient condition for the Iwasawa invariant $\lambda _p(k)$ of the cyclotomic $\mathbb {Z}_p$-extension of $k$ to be zero. The purpose of this paper is to study the case $p=3$ of this result and give new examples of $k$ with $\lambda _3(k)=0$, by using information on the initial layer of the cyclotomic $\mathbb {Z}_3$-extension of $k$.

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