Zeta of x²+y²=1 over finite fields

Wednesday, July 18th, 2012 | Author:

I must admit that I have a weak background in elementary number theory. A few weeks ago I wanted to count the number of points of the affine circle $x^2+y^2=1$ over finite fields, by counting the point of the completed curve and the points at infinity. There one needs to decide whether a finite field with $p^k$ elements contains roots of -1 or not.

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