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Keywords:
ternary quadratic forms; Gauss reciprocity law; Hasse-Minkowski theorem
ternary quadratic forms; Gauss reciprocity law; Hasse-Minkowski theorem
Summary:
For a ternary quadratic form over the rational numbers, we characterize the set of rational numbers represented by that form over the rational numbers. Consequently, we reprove the classical fact that any positive definite integral ternary quadratic form must fail to represent infinitely many positive integers over the rational numbers. Our proof uses only the quadratic reciprocity law and the Hasse-Minkowski theorem, and is elementary.
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