Positive values of inhomogeneous quaternary quadratic forms, I

Abstract

Let Q ( x 1 , …, x n ) be an indefinite quadratic form in n -variables with real coefficients, determinant D ≠ 0 and signature ( r , s ), r + s = n . Then it is known (e.g. see Blaney [2]) that there exist constants Γ r , s depending only on r and s such for any real numbers c 1 , …, c n we can find integers x 1 , …, x n satisfying