Thue equations and CM-fields

Abstract

Abstract. We obtain a polynomial type upper bound for the size of the integral solutions of Thue equations F (X, Y ) = b defined over a totally real number field K, assuming that F (X, 1) has a root α such that K(α) is a CM-field. Furthermore, we give an algorithm for the computation of the integral solutions of such an equation.

On some norm inequalities and discriminant inequalities in CM-fields

“…The above norm inequalities were applied in Győry and Lovász [7], Győry [11], and Aubry and Poulakis [1] to diophantine equations, and in Győry [8], [9], [10], [12], [13], Schinzel [24], and Győry, Hajdu and Tijdeman [14] to irreducible polynomials.…”