# The Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\sqrt{-3})$

I'm now on a research about the Iwasawa $$\lambda$$-invariants of the cyclotomic $$\mathbb{Z}_p$$-extensions of number fields. And it happens that the cyclotomic $$\mathbb{Z}_3$$-extension of $$\mathbb{Q}(\sqrt{-3})$$ is an elementary but important case for my early research.

But I couldn't found a literature on it yet, and also I'm not an expert in this area yet so I'm not used to computing invariants by myself.

So can you please give any information about this $$\lambda$$-invariant?

Thank you.

• Washington 13.22 shows that no class group in this tower is divisible by $p=3$ so $\lambda=\mu=0$. – Chris Wuthrich Jan 16 at 9:14
• Thank you very much. Your answer will be very helpful. Thank you again! – gualterio Jan 16 at 12:00