An Extension of Meyer's Theorem on Indefinite Ternary Quadratic Forms

Abstract

Let f be a ternary quadratic form whose matrix F has integral elements with g.c.d. 1, that is, an improperly or properly primitive form according as all diagonal elements are even or not. Let d be the determinant of f (denoted by ) Ω, the g.c.d. of the 2-rowed minors of F. Then d = Ω2 Δ determines an integer Δ. Two forms f in the same genus have the same invariants Ω, Δ, d. The form whose matrix is adj F/Ω, is called the reciprocal form of f.