Displaying similar documents to “Rational zeros of two quadratic forms”

On ternary quadratic forms over the rational numbers

Amir Jafari, Farhood Rostamkhani (2022)

Czechoslovak Mathematical Journal

Similarity:

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.