A note on pencils of norm-form equations

Prajeet Bajpai; Michael A. Bennett

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arXiv · 2104.04544

A note on pencils of norm-form equations

Prajeet Bajpai·Michael A. Bennett

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Abstract

We find all solutions to the parametrized family of norm-form equations $x^3-(t^3-1)y^3+3(t^3-1)xy+(t^3-1)^2 = \pm 1$ studied by Amoroso, Masser and Zannier. Our proof relies upon an appeal to lower bounds for linear forms in logarithms and various elementary arguments.

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Prajeet Bajpai, Michael A. Bennett. 2021-04-09. A note on pencils of norm-form equations. https://arxiv.org/abs/2104.04544

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