A Theorem about Three Quadratic Forms

Abstract

σ1[x] · σ2[x]. Therefore, if we find s > 0 such that σ[x] < 0 for some x satisfying σ2[x]/σ1[x] = s 2, we get a contradiction with (1.1). Consider the set S ⊂ (0,∞) × (0,∞) consisting of all pairs (s, t) such that σs[x] < 0 for some x satisfying σ2[x]/σ1[x] = t 2. We want to show that (α,α) ∈ S for some α > 0, which gives us the contradiction. Since all… (More)