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Effective results for Diophantine equations over finitely generated domains

Attila BérczesJan-Hendrik EvertseKálmán Győry — 2014

Acta Arithmetica

Let A be an arbitrary integral domain of characteristic 0 that is finitely generated over ℤ. We consider Thue equations F(x,y) = δ in x,y ∈ A, where F is a binary form with coefficients from A, and δ is a non-zero element from A, and hyper- and superelliptic equations f ( x ) = δ y m in x,y ∈ A, where f ∈ A[X], δ ∈ A∖0 and m 2 . Under the necessary finiteness conditions we give effective upper bounds for the sizes of the solutions of the equations in terms of appropriate representations for A, δ, F, f, m. These...

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