On the resolution of inhomogeneous norm form equations in two dominating variables

Gaál, István

doi:10.1090/S0025-5718-1988-0942162-6

On the resolution of inhomogeneous norm form equations in two dominating variables
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Math. Comp. 51 (1988), 359-373 Request permission

Abstract:

Applying Baker’s well-known method and the reduction procedure described by Baker and Davenport, we give a numerical algorithm for finding all solutions of inhomogeneous Thue equations of type \[ {N_{K/Q}}(x + \alpha y + \lambda ) = 1\] in the variables $x,y \in Z$ and $\lambda \in {Z_K}$ with $\lceil \lambda \rceil < (\max |x|,|y|){)^{1/2}}$, where $K = Q(\alpha )$ is a totally real cubic field.

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Résultats Effectifs sur la Représentation des Entiers par des Formes Décomposables

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On Diophantine Equations of Norm Form Type

Effective Bounds for Linear Forms with Algebraic Coefficients in Archimedean and p-Adic Metrics

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