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The p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems

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Iwasawa logarithm and analytic continuation

I am reading Number Theory vol. 1 by Henri Cohen (among other things) and I am curious about the Iwasawa logarithm. Let $\mathbb{C}_p$ be the completion of the algebraic closure of $\mathbb{Q}_p$. Le …
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