Simple families of Thue inequalities

Lettl, Günter; Pethő, Attila; Voutier, Paul

doi:10.1090/S0002-9947-99-02244-8

Simple families of Thue inequalities
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by Günter Lettl, Attila Pethő and Paul Voutier

Trans. Amer. Math. Soc. 351 (1999), 1871-1894

DOI: https://doi.org/10.1090/S0002-9947-99-02244-8

Published electronically: January 26, 1999

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Abstract:

We use the hypergeometric method to solve three families of Thue inequalities of degree 3, 4 and 6, respectively, each of which is parametrized by an integral parameter. We obtain bounds for the solutions, which are astonishingly small compared to similar results which use estimates of linear forms in logarithms.

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