On Thue equations of splitting type over function fields
نویسندگان
چکیده
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.
منابع مشابه
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...
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