Quadratic Diophantine Inequalities Original Research Article

We consider systems of quadratic diophantine inequlities. For example, suppose that Q1 and Q2 are real diagonal quadratic forms in s variables, where one has sgreater-or-equal, slanted10. Suppose also that every form αQ1+βQ2 with (α, β)set membership, variantimage2\{0} has at least 5 nonzero coefficients, one irrational coefficient, at least one negative coefficient, and at least one positive coefficient. Then for any var epsilon>0, there exists a nonzero integral vector xset membership, variantimages such that Q1(x)