Systems of quadratic diophantine inequalities
Systems of quadratic diophantine inequalities
Let Q 1 ,⋯,Q r be quadratic forms with real coefficients. We prove that for any ϵ>0 the system of inequalities |Q 1 (x)|<ϵ,⋯,|Q r (x)|<ϵ has a nonzero integer solution, provided that the system Q 1 (x)=0,⋯,Q r (x)=0 has a nonsingular real solution and all forms in the …