Solving simultaneously Thue equations in the almost totally imaginary case

الأصل · EN

Let α be an algebraic number of degree d≥ 3 having at most one real conjugate and let K be the algebraic number field Q(α). For any unit ε of K such that Q(αε)=K, we consider the irreducible polynomial fε(X)∈Z[X] such that fε(αε)=0. Let Fε(X,Y)= Yᵈfε(X/Y)∈Z[X,Y] be the associated binary form. For each positive integer m, we exhibit an effectively computable bound for the solutions (x,y,ε) of the diophantine equation |Fε(x,y)|≤ m.