Diophantine approximation of ternary linear forms

The paper gives an efficient method for finding arbitrarily many solutions in integers x, y, z of the Diophantine inequality x ay z max(y2, z2) c, where a defines a totally real cubic field F over the rationals, the numbers 1, a, form an integral basis for F, and c is a constant which can be calculated in terms of parameters of the method. For certain values of c, the method generates all solutions of the inequality.