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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 $\nu$?

  • 5
    Rather than delete the question, why don't you post the answer and then accept it. Then others can benefit from your insight.2011-04-08

1 Answers 1

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