Diophantine approximation of ternary linear forms

Abstract:

The paper gives an efficient method for finding arbitrarily many solutions in integers x, y, z of the Diophantine inequality $|x + \alpha y + \beta z|\max ({y^2},{z^2}) < c$, where $\alpha$ defines a totally real cubic field F over the rationals, the numbers 1, $\alpha ,\beta$ 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.