On Thue Equations of Splitting Type over Function Fields

On Thue equations of splitting type over function fields

In this paper we consider Thue equations of splitting type over the ring k[T ], i.e. they have the form X(X − p1Y ) · · · (X − pd−1Y )− Y d = ξ, with p1, . . . , pd−1 ∈ k[T ] and ξ ∈ k. In particular we show that such Thue equations have only trivial solutions provided the degree of pd−1 is large, with respect to the degree of the other parameters p1, . . . , pd−2.

Diophantine Equations over Global Function Fields II: R-Integral Solutions of Thue Equations

On a Parametric Family of Thue Inequalities over Function Fields

is called a Thue equation, due to Thue [22] who proved, in the case R = Z, that such an equation has finitely many solutions. In the last decade, starting with the result of Thomas in [21], several families (at the moment up to degree 8; see [9] and the references mentioned therein) of Thue equations have been considered, where the coefficients of the form Fc(X,Y ) depend on an integral paramet...

Thomas' Family of Thue Equations Over Imaginary Quadratic Fields

Thue equations and CM-fields

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.