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Is the statement of Iwasawa's theorem that for every number field $K$ there are $\mu$, $\lambda$ and $\nu$ such that for every $\mathbb{Z}_p$ extension $K_{\infty}$, the class number of any big enough level, say $n$, is $\lambda n+ \mu p^n +\nu$?

Or is the statement that for every $\mathbb{Z}_p$ extension $K_{\infty}$ there are $\mu$ $\lambda$ and $\nu$?

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Never mind. I figured it out. I'm not sure how to delete the question, though. – Nicole Apr 7 '11 at 23:01
Rather than delete the question, why don't you post the answer and then accept it. Then others can benefit from your insight. – Alex B. Apr 8 '11 at 0:09

As you probably figured out, the quantities $\lambda,$ $\mu$, and $\nu$ depend on the $\mathbb Z_p$-extension.

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