The Weil bounds
نویسنده
چکیده
• Y 2 −X is reducible, • Y 2 − αX is irreducible, but not absolutely irreducible, • Y 2 −X + 1 is absolutely irreducible. To see the last item, note that any factorization of H(X,Y ) = Y −X+1 in F[X,Y ] is also a factorization of H(X,Y ) in K[Y ], where K is the field F(X), and thus the factorization must be of the form (Y −a(X))(Y + a(X)), where a(X) ∈ K satisfies a(X) = X − 1. But this cannot be. We can now state the Weil bound.
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