What Is the P-adic Volume of the P-adic Circle x² + y² = 1?

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Find the p-adic volume of the p-adic circle x^2 + y^2 = 1.

This isn't hw.
 
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>Find the p-adic volume of the p-adic circle x^2 + y^2 = 1.

p-adic pi?
 
I would guess you'd need measure and integration. I think Koblitz's P-adic numbers, p-adic analysis, and zeta-functions covers this. That said, are you sure this curve encloses a finite area?
 
I'm not even sure what a p-adic number is. The professor handed out this sheet for us to "enjoy." It's not collected or anything. It's just for us - for fun. This was one of the questions on the sheet, and it doesn't elaborate on it at all. So I have no idea if it's a finite area.
 

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